JFEC Special Issue for Peter Christoffersen

No, I have not gone into seclusion. Well actually I have, but not intentionally and certainly not for lack of interest in the blog. Just the usual crazy time of year, only worse this year for some reason. Anyway I'll be back very soon, with lots to say! But here's something important and timely, so it can't wait:

Journal of Financial Econometrics

Call for Papers

Special Issue in Honor of Peter Christoffersen

The Journal of Financial Econometrics is organizing a special issue in memory of Professor Peter
Christoffersen, our friend and colleague, who passed away in June 2018. Peter held the TMX Chair in Capital Markets and a Bank of Canada Fellowship and was a widely respected member of the Rotman School at the University of Toronto since 2010. Prior to 2010, Peter was a valued member of the Desautels Faculty of Management at McGill University. In addition to his transformative work in econometrics and volatility models, financial risk and financial innovation had been the focus of Peter’s work in recent years.

We invite paper submissions on topics related to Peter’s contributions to Finance and Econometrics. We are particularly interested in papers related to the following topics:

1)   The use of option-implied information for forecasting; Rare disasters and portfolio
management; Factor structures in derivatives and futures markets.

2)   Volatility, correlation, extreme events, systemic risk and Value-at-Risk modeling for
financial market risk management.

3)   The econometrics of digital assets; Big data and Machine Learning.

To submit a paper, authors should login to the Journal of Financial Econometrics online submission system and follow the submission instructions as per journal policy.  The due date for submissions is June 30, 2019.  It is important to specify in the cover letter that the paper is submitted to the special issue in honor of Peter Christoffersen, otherwise your paper will not be assigned to the guest editors.

Guest Editors

•    Francis X. Diebold, University of Pennsylvania

•    René Garcia, Université de Montréal and Toulouse School of Economics

•    Kris Jacobs, University of Houston

Long Memory / Scaling Laws in Return Volatility

The 25-year accumulation of evidence for long memory / fractional integration / self-similarity / scaling laws in financial asset return volatility continues unabated.  For the latest see this nice new paper from Bank of Portugal, in particular its key Table 6. Of course the interval estimates of the fractional integration parameter "d" are massively far from both 0 and 1 -- that's the well-known long memory. But what's new and interesting is the systematic difference in the intervals depending on whether one uses absolute or range-based volatility. The absolute d intervals tend to be completely below 1/2 (0<d<1/2 corresponds to covariance-stationary dynamics), whereas the range-based d intervals tend to include 1/2 (1/2<d<1 corresponds to mean-reverting but not covariance- stationary dynamics, due to infinite unconditional variance). 

Realized vol based on the range is less noisy than realized vol based on absolute returns. But least noisy of all, and not considered in the paper above, is realized vol calculated directly from high-frequency return data (HFD-vol), as done by numerous authors in recent decades. Interestingly, recent work for HFD-vol also reports d intervals that tend to poke above 1/2. See this earlier post.

Factor Model w Time-Varying Loadings

Markus Pelger has a nice paper on factor modeling with time-varying loadings in high dimensions. There are many possible applications. He applies it to level-slope-curvature yield-curve models. 

For me another really interesting application would be measuring connectedness in financial markets, as a way of tracking systemic risk. The Diebold-Yilmaz (DY) connectedness framework is based on a high-dimensional VAR with time-varying coefficients, but not factor structure. An obvious alternative in financial markets, which we used to discuss a lot but never pursued, is factor structure with time-varying loadings, exactly in Pelger! 

It would seem, however, that any reasonable connectedness measure in a factor environment would need to be based not only time-varying loadings but also time-varying idiosynchratic shock variances, or more precisely a time-varying noise/signal ratio (e.g., in a 1-factor model, the ratio of the idiosyncratic shock variance to the factor innovation variance). That is, connectedness in factor environments is driven by BOTH the size of the loadings on the factor(s) AND the amount of variation in the data explained by the factor(s). Time-varying loadings don't really change anything if the factors are swamped by massive noise. 

Typically one might fix the factor innovation variance for identification, but allow for time-varying idiosyncratic shock variance in addition to time-varying factor loadings. It seems that Pelger's framework does allow for that. Crudely, and continuing the 1-factor example, consider y_t  =  lambda_t  f_t  +  e_t. His methods deliver estimates of the time series of loadings lambda_t and factor f_t, robust to heteroskedasticity in the idiosyncratic shock e_t. Then in a second step one could back out an estimate of the time series of e_t and fit a volatility model to it. 
Then the entire system would be estimated and one could calculate connectedness measures based, for example, on variance decompositions as in the DY framework. 

Gu-Kelly-Xiu and Neural Nets in Economics

I'm on record as being largely unimpressed by the contributions of neural nets (NN's) in economics thus far. In many economic environments the relevant non-linearities seem too weak and the signal/noise ratios too low for NN's to contribute much. 

The Gu-Kelly-Xiu paper that I mentioned earlier may change that. I mentioned their success in applying machine-learning methods to forecast equity risk premia out of sample. NN's, in particular, really shine. The paper is thoroughly and meticulously done. 

This is potentially a really big deal.

Machine Learning, Volatility, and the Interface

Just got back from the NBER Summer Institute. Lots of good stuff happening in the Forecasting and Empirical Methods group. The program, with links to papers, is here.

Lots of room for extensions too. Here's a great example. Consider the interface of the Gu-Kelly-Xiu and Bollerslev-Patton-Quagvleg papers. At first you might think that there is no interface. 

Kelly-Xiu is about using off-the-shelf machine-learning methods to model risk premia in financial markets; that is, to construct portfolios that deliver superior performance. (I had guessed they'd get nothing, but I was massively wrong.) Bollerslev et al. is about predicting realized covariance by exploiting info on past signs (e.g., was yesterday's covariance cross-product pos-pos, neg-neg, pos-neg, or neg-pos?). (They also get tremendous results.)

But there's actually a big interface.

Note that Kelly-Xiu is about conditional mean dynamics -- uncovering the determinants of expected excess returns. You might expect even better results for derivative assets, as the volatility dynamics that drive options prices may be nonlinear in ways missed by standard volatility models. And that's exactly the flavor of the Bollerslev et al. results -- they find that a tree structure conditioning on sign is massively successful.

But Bollerslev et al. don't do any machine learning. Instead they basically stumble upon their result, guided by their fine intuition. So here's a fascinating issue to explore: Hit the Bollerslev et al. realized covariance data with machine learning (in particular, tree methods like random forests) and see what happens. Does it "discover" the Bollerslev et al. result? If not, why not, and what does it discover? Does it improve upon Bollerslev et al.?

Machines Learning Finance

FRB Atlanta recently hosted a meeting on "Machines Learning Finance". Kind of an ominous, threatening (Orwellian?) title, but there were lots of (non-threatening...) pieces. I found the surveys by Ryan Adams and John Cunningham particularly entertaining. A clear theme on display throughout the meeting was that "supervised learning" -- the main strand of machine learning -- is just function estimation, and in particular, conditional mean estimation. That is, regression. It may involve high dimensions, non-linearities, binary variables, etc., but at the end of the day it's still just regression. If you're a regular No Hesitations reader, the "insight" that supervised learning = regression will hardly be novel to you, but still it's good to see it disseminating widely.

An Art Market Return Index

Rare and collectible goods, from fine art to fine wine, have many interesting and special aspects. Some are shared and some are idiosyncratic.

From the vantage point of alternative investments (among other things), it would be useful to have high-frequency indices for those asset markets, just as we do for traditional "financial" asset markets like equities.

Along those lines, in "Monthly Art Market Returns" Bocart, Ghysels, and Hafner develop a high-frequency measurement approach, despite the fact that art sales generally occur very infrequently. Effectively they develop a mixed-frequency repeat-sales model, which captures the correlation between art prices and other liquid asset prices that are observed much more frequently. They use the model to extract a monthly art market return index, as well as sub-indices for contemporary art, impressionist art, etc.

Quite fascinating and refreshingly novel.

Classic Jacod (1994) Paper

J. Financial Econometrics will soon publish Jean Jacod's brilliant and beautiful 1994 paper, "Limit of Random Measures Associated with the Increments of a Brownian Semimartingale", which I just had the pleasure of reading for the first time. (Ungated version here.) Along with several others, I was asked to supply some comments for the issue's introduction. What follows is adapted from those comments, providing some historical background. (Except that it's not really historical background -- keep reading...)

Jacod's paper effectively lays the foundation for the vast subsequent econometric "realized volatility" (empirical quadratic variation) literature of the past twenty years.  Reading it leads me to recall my early realized volatility work with Torben Andersen and Tim Bollerslev in the late 1990's and early 2000's. It started in the mid-1990's at a meeting of the NBER Asset Pricing Program, where I was the discussant for a paper of theirs, eventually published as Andersen and Bollerslev (1998). They were using realized volatility as the "realization" in a study of GARCH volatility forecast accuracy, and my discussion was along the lines of, "That's interesting, but I think you've struck gold without realizing it -- why not skip the GARCH and instead simply characterize, model, and forecast realized volatility directly?".

So we decided to explore realized volatility directly. Things really took off with Andersen et al. (2001) and Andersen et al. (2003). The research program was primarily empirical, but of course we also wanted to advance the theoretical foundations. We knew some relevant stochastic integration theory, and we made progress culminating in Theorem 2 of Andersen et al. (2003). Around the same time, Ole Bardorff-Nielsen and Neil Shephard were also producing penetrating and closely-related results (most notably Barndorff-Nielsen and Shephard, 2002). Very exciting early times.

Now let's return to Jacod's 1994 paper, and consider it against the above historical background of early econometric realized volatility papers. Doing so reveals not only its elegance and generality, but also its prescience: It was written well before the "historical background"!! One wonders how it went unknown and unpublished for so long.

References

Andersen, T. G. and T. Bollerslev (1998), "Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts," International Economic Review, 39, 885-905.

Andersen, T.G., T. Bollerslev, F.X. Diebold, and P. Labys (2001), "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, 96, 42-55.

Andersen, T.G., T. Bollerslev, F.X. Diebold, and P. Labys (2003), "Modeling and Forecasting Realized Volatility," Econometrica, 71, 579-625.

Barndorff-Nielsen, O. and N. Shephard (2002), "Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models," Journal of the Royal Statistical Society, 64,
253-280.

Jacod, J. (1994), "Limit of Random Measures Associated with the Increments of a Brownian Semimartingale," Manuscript, Institute de Mathematiques de Jussieu, Universite Pierre et Marie Curie, Paris.

The Rate of Return on Everything

Jorda, Knoll, Kuvshinov, Schularick and Taylor deliver more than just a memorable title, "The Rate of Return on Everything, 1870-2015". (Dec 2017 NBER version here; earlier ungated June 2017 version here.) Their paper is a fascinating exercise in data construction and analysis. It goes well beyond, say, the earlier and also-fascinating Dimson et al. (2002) book, by including housing, among other things.

Caveat emptor: In this case two words suffice -- survivorship bias. Jorda et al. are well aware of it, and they work hard to assess and address it. But still.

Commodity Connectedness

Forthcoming paper here. 
We study connectedness among the major commodity markets, summarizing and visualizing the results using tools from network science.

Among other things, the results reveal clear clustering of commodities into groups closely related to the traditional industry taxonomy, but with some notable differences.

Many thanks to Central Bank of Chile for encouraging and supporting the effort via its 2017 Annual Research Conference.

Exogenous vs. Endogenous Volatility Dynamics

I always thought putting exogenous volatility dynamics in macro-model shocks was a cop-out.  Somehow it seemed more satisfying for volatility to be determined endogenously, in equilibrium.  Then I came around:  We allow for shocks with exogenous conditional-mean dynamics (e.g., AR(1)), so why shouldn't we allow for shocks with exogenous conditional-volatility dynamics?  Now I might shift back, at least in part, thanks to new work by Sydney Ludvigson, Sai Ma, and Serena Ng, "Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?", which attempts to sort things out. The October 2016 version is here.  It turns out that real (macro) volatility appears largely endogenous, whereas nominal (financial market) volatility appears largely exogenous. 

Dense Data for Long Memory

From the last post, you might think that efficient learning about low-frequency phenomena requires tall data. Certainly efficient estimation of trend, as stressed in the last post, does require tall data. But it turns out that efficient estimation of other aspects of low-frequency dynamics sometimes requires only dense data. In particular, consider a pure long memory, or "fractionally integrated", process, \( (1-L)^d x_t = \epsilon_t \), 0 < \( d \) < 1/2. (See, for example, this or this.) In a general \( I(d) \) process, \(d\) governs only low-frequency behavior (the rate of decay of long-lag autocorrelations toward zero, or equivalently, the rate of explosion of low-frequency spectra toward infinity), so tall data are needed for efficient estimation of \(d\). But in a pure long-memory process, one parameter (\(d\)) governs behavior at all frequencies, including arbitrarily low frequencies, due to the self-similarity ("scaling law") of pure long memory. Hence for pure long memory a short but dense sample can be as informative about \(d\) as a tall sample. (And pure long memory often appears to be a highly-accurate approximation to financial asset return volatilities, as for example in ABDL.)

SoFiE 2016 Hong Kong (and 2017 New York)

Hats off to all those who helped make the Hong Kong SoFiE meeting such a success. Special thanks (in alphabetical order) to Charlotte Chen, Yin-Wong Cheung, Jianqing Fan, Eric Ghysels, Ravi Jagannathan, Yingying Li, Daniel Preve, and Giorgio Valente. The conference web site is here. 

Mark your calendars now for what promises to be a very special tenth-anniversary meeting next year in New York, hosted by Rob Engle at NYU's Stern School. The dates are June 20-23, 2017.

SoFiE 2016 Hong Kong

Still not too late to register!  I hope to see you there.

REGISTRATION_9th Annual SoFiE Conference_June 14-17, 2016, Hong Kong

REGISTRATION 9th Annual Society for Financial Econometrics (SoFiE) Conference  June 15-17, 2016   and   Pre-Conference for Young Scholars June 14, 2016 Hosted by the Department of Economics and Finance & the Global Research Unit (GRU) at City University of Hong Kong _________________________________________________________________________ CONFERENCE WEBSITE & REGISTRATION https://www.cb.cityu.edu.hk/conference/2016-sofie/ Preliminary Program ___________________________________________________ HALBERT WHITE JR. MEMORIAL JFEC INVITED LECTURE René Garcia, EDHEC Business School INVITED SPEAKERS Harrison Hong, Princeton University Michael McCracken, Federal Reserve Bank of St. Louis Per Mykland, University of Chicago Olivier Scaillet, University of Geneva & Swiss Finance Institute Hao Zhou, PBCSF, Tsinghua University INVITED SPEAKER, Pre-Conference Francis X. Diebold, University of Pennsylvania CONFERENCE LOCATION City University of Hong Kong LOCAL ORGANIZERS Yingying Li, Hong Kong University of Science and Technology Daniel Preve, City University of Hong Kong Giorgio Valente, City University of Hong Kong PROGRAM CHAIR Jianqing Fan, Princeton University PROGRAM COMMITTEE            Torben Andersen, Northwestern University           Frank Kleibergen, University of Amsterdam            Heather Anderson, Monash University           Ralph Koijen, London Business School            Elena Andreou, University of Cyprus           Siem Jan Koopman, VU University Amsterdam            Jushan Bai, Columbia University           Stephen Kou, National University of Singapore            Gurdip Bakshi, University of Maryland           David Lando, Copenhagen Business School            Federico Bandi, Johns Hopkins University           Jia Li, Duke University            David Bates, University of Iowa           Yingying Li, Hong Kong University of Science & Technology            Luc Bauwens, Universite Catholique de Louvain           Haitao Li, Cheung Kong Graduate School of Business            Luca Benzoni, Federal Reserve Bank of Chicago           Yuan Liao, University of Maryland            Tim Bollerslev, Duke University           Chenghu Ma, Fudan University            Laurent Calvet, HEC Paris           Loriano Mancini, EPFL            Marine Carrasco, University of Montreal           Cecilia Mancini, University of Florence            Rong Chen, Rutgers University           Simone Manganelli, European Central Bank            Mikhail Chernov, London School of Economics & UCLA           Nour Meddahi,  Toulouse School of Economics            Peter Christoffersen, University of Toronto           Per Mykland, University of Chicago            Riccardo Colacito, University of North Carolina, Chapel Hill           Joon Park, Indiana University             Pierre Collin-Dufresne, EPFL           Andrew Patton, NYU Stern            Valentina Corradi, University of Surrey            Tarun Ramadorai, University of Oxford            Walter Distaso, Imperial College Business School           Eric Renault, Brown University            Dobrislav Dobrev, Federal Reserve Board           Michael Rockinger, University of Lausanne            Yanqin Fan, University of Washington, Seattle           Jeroen Rombouts, ESSEC Business School            Patrick Gagliardini, University of Lugano           Mathieu Rosenbaum, University Pierre et Marie Curie (Paris 6)            Rene Garcia, EDHEC Business School           Barbara Rossi, Pompeu Fabra University            Eric Ghysels, University of North Carolina, Chapel Hill           Jeffrey Russell, University of Chicago            Sílvia Goncalves, University of Montreal           Olivier Scaillet, University of Geneva & SFI            Christian Gourieroux, University of Toronto           Paul Schneider, University of Lugano & SFI            Anthony Hall, University of Technology Sydney           Enrique Sentana, CEMFI            Wolfgang Hardle, Humboldt University           George Tauchen, Duke University            Joel Hasbrouck, NYU Stern           Allan Timmermann, University of California, San Diego            Nikolaus Hautsch, University of Vienna           Viktor Todorov, Northwestern University            Stan Hurn, Queensland University of Technology            Fabio Trojani, University of Lugano & SFI            Ravi Jagannathan, Northwestern University            Ruey Tsay, Duke University of Chicago            Christopher S. Jones, University of Southern California             Bas J.M. Werker, Tilburg University            Scott Joslin, University of Southern California            Dacheng Xiu, University of Chicago            Raymond Kan, University of Toronto            Jun Yu, Singapore Management University            Kamhon Kan, Academia Sinica            Zhengjun Zhang, University of Wisconsin            Bryan Kelly, University of Chicago            Lan Zhang, University of Illinois at Chicago            Lutz Kilian, University of Michigan            Harold H. Zhang, University of Texas at Dallas            Robert Kimmel, National University of Singapore            Xunyu Zhou, Oxford University

Coolest Paper at 2015 Jackson Hole

The Faust-Leeper paper is wild and wonderful.  The friend who emailed it said, "Be prepared, it’s very different but a great picture of real-time forecasting..." He got it right.

Actually his full email was, "Be prepared, it’s very different but a great picture of real-time forecasting, and they quote Zarnowitz." (He and I always liked and admired Victor Zarnowitz. But that's another post.)

The paper shines its light all over the place, and different people will read it differently. I did some spot checks with colleagues. My interpretation below resonated with some, while others wondered if we had read the same paper. Perhaps, as with Keynes, we'll never know exactly what Faust-Leeper really, really, really meant.

I read Faust-Leeper as speaking to factor analysis in macroeconomics and finance, arguing that dimensionality reduction via factor structure, at least as typically implemented and interpreted, is of limited value to policymakers, although the paper never uses wording like "dimensionality reduction" or "factor structure".

If Faust-Leeper are doubting factor structure itself, then I think they're way off base. It's no accident that factor structure is at the center of both modern empirical/theoretical macro and modern empirical/theoretical finance. It's really there and it really works.

Alternatively, if they're implicitly saying something like this, then I'm interested:

Small-scale factor models involving just a few variables and a single common factor (or even two factors like "real activity" and "inflation") are likely missing important things, and are therefore incomplete guides for policy analysis. 

Or, closely related and more constructively: 

We should cast a wide net in terms of the universe of observables from which we extract common factors, and the number of factors that we extract. Moreover we should examine and interpret not only common factors, but also allegedly "idiosyncratic" factors, which may actually be contemporaneously correlated, time dependent, or even trending, due to mis-specification.

Enough.  Read it for yourself.

[General note: My use of terms like "factor modeling" throughout this post should be broadly interpreted to include not only explicit reduced-form statistical/econometric dynamic factor modeling, but also structural DSGE modeling.]  

Christensen on Term Structure Modeling at EUI

Jens Christensen will give a Euro-Area Business Cycle Network three-day course at EUI, September 7-9. Jens is fantastic. Plus it's Florence in early September. It's not too late to register!

Course Syllabus

Recommended Reading List

Course Schedule

List of Participants (as of 05.08.2015)

Logistical Information

Rebonato on Bond-Yield Econometrics

Riccardo Rebonato (R) has a fascinating new paper, which builds on important earlier work of Cieslak and Povala (2010) (CP). 

The cool thing about CP is the way it advances and blends certain aspects of both the spanning literature ("all information of relevance for yield prediction is embedded in the current term structure," e.g. via forward-rate tent functions as in Cochrane-Piazessi (2004)), and the non-spanning literature ("not all information of relevance for yield prediction is embedded in the current term structure," e.g. because certain macro variables seem to help predict risk premia, as in Ludvidson and Ng (2009)).

In turn, the cool thing about R is its insightful high-frequency / low-frequency interpretation of CP, with the macro predictors of primary relevance at low frequencies. 

Adapted from the R abstract:

This paper presents a simple reformulation of the restricted CP return-predicting factor which retains by construction exactly the same (impressive) explanatory power as the original one, but affords an alternative and attractive interpretation. What determines future returns, the new factor shows, is ... the distance of the yield-curve level and the slope not from fixed reference levels, but from conditional ones determined by ... long-term inflation.

I'm reminded of key early work by Kozicki and Tinsley (2001) on market perceptions of central bank credibility providing low-frequency anchoring for long yields.

More generally, high-frequency / low-frequency decompositions have a long and distinguished history in time-series econometrics, from cycle / trend real-output decompositions in macro-econometrics (e.g., Cochrane (1988)) to short-run / long-run volatility decompositions in financial econometrics (e.g., the "component GARCH" model of Engle and Lee (1999)).

A final thought: Bauer and Hamilton (2015) have recently questioned the entire non-spanning literature. Perhaps I'll cover that in a subsequent post, and its relation to CP and R (e.g., why worry about blending the spanning and non-spanning approaches if the non-spanning approach is suspect?).

Measuring and Monitoring Connectedness

I'm at the IMF soon for a couple days of lecturing on Diebold-Yilmaz's Connectedness. It was published earlier this year, and preparing for the IMF jogged my memory: I brilliantly forgot to announce it in a No Hesitations post. Anyway, it's available at the usual online shops (where you can also read the T.O.C. and first chapter), or directly from Oxford University Press. There's also a web site. Special thanks to Eric Ghysels, who put us in touch with our fine editor, Scott Parris. 

Online Volatility Data and Labs

I am reminded that I had planned to post on data/analysis sites that focus on financial asset return volatility measurement and modeling.

To my mind, the key trio is implied vol, GARCH vol, and realized vol. For implied vol it's the VIX at CBOE. For GARCH vol it's Rob Engle's V-Lab at NYU. For realized vol it's Neil Shephard's Realized Library at Oxford.

Yes, conspicuously missing is stochastic volatility. It's an academic simulator's paradise, but largely missing from serious/practical industry application. It's no accident; the benefit/cost ratio is just too low to excite many real financial-market modelers. One could argue that ten years from now things will look different. Perhaps, but I'm not at all sure. 

Bond Yields, Macro Fundamentals, and Policy

Greetings my friends from Eurovision in Vienna. Yes, OK, that's not exactly the real reason I'm here, but still...

As I said in an earlier post that stressed DNS/AFNS yield-curve modeling with the zero lower bound imposed, "although Nelson-Siegel is almost thirty years old, and DNS/AFNS is almost a teenager, interesting and useful new variations keep coming." Another intriguing DNS/AFNS literature strand concerns the interaction of bond yields and macro fundamentals. That's hardly a new area, but recent work has some interesting twists.

Mesters, Schwaab and Koopman (2015) (MSK) focus on the effects of central bank policy on bond yields. There's lots of interesting new tech (stochastic volatility in measurement errors, interactions with non-Gaussian variables, a novel importance sampler for likelihood evaluation, ...). But most interestingly, MSK explore not only conventional policy tools like the overnight lending rate, but also direct measures of bond purchases.

MSK build on Diebold, Rudebusch and Aruoba (2006) (DRA), but the DRA emphasis is different. DRA were interested in whether and how the yield curve is linked to "standard" macro fundamentals. So DRA emphasized inflation, with an eye toward the yield curve level, and real activity, with an eye toward the yield curve slope. DRA also included an overnight lending rate, but certainly no measures of bond purchases.

Lots of interesting MSK-style work remains to be done. For example, someone needs to do an MSK-style analysis in a shadow-rate model that respects the zero lower bound and imposes no-arb. Also, someone needs to explore both causal directions more thoroughly. (Of course central bank bond purchases might influence the yield curve, but so too does the yield curve influence central bank bond purchases.)