## Sunday, August 20, 2017

### Bayesian Random Projection (More on Terabytes of Economic Data)

Some additional thoughts related to Serena Ng's World Congress piece (earlier post here, with a link to her paper):

The key newish dimensionality-reduction strategies that Serena emphasizes are random projection and leverage score sampling.  In a regression context both are methods for optimally approximating an NxK "X matrix" with an Nxk X matrix, where k<<K. They are very different and there are many issues. Random projection delivers a smaller X matrix with columns that are linear combinations of those of the original X matrix, as for example with principal-component regression, which can sometimes make for difficult interpretation.  Leverage score sampling, in contrast, delivers a smaller X matrix with columns that are simply a subset of those of those of the original X matrix, which feels cleaner but has issues of its own.

Anyway, a crucial observation is that for successful predictive modeling we don't need deep interpretation, so random projection is potentially just fine -- if it works, it works, and that's an empirical matter.  Econometric extensions  (e.g., to VAR's) and evidence (e.g., to macro forecasting) are just now emerging, and the results appear encouraging.  An important recent contribution in that regard is Koop, Korobilis, and Pettenuzzo (in press), which significantly extends and applies earlier work of Guhaniyogi and Dunson (2015) on Bayesian random projection ("compression").  Bayesian compression fits beautifully in a MCMC framework (again see Koop et al.), including model averaging across multiple random projections, attaching greater weight to projections that forecast well.  Very exciting!

## Monday, August 14, 2017

### Analyzing Terabytes of Economic Data

Serena Ng's World Congress piece is out as an NBER w.p.  It's been floating around for a long time, but just in case you missed it, it's a fun and insightful read:

Opportunities and Challenges: Lessons from Analyzing Terabytes of Scanner Data
by Serena Ng  -  NBER Working Paper #23673.
http://papers.nber.org/papers/w23673

(Ungated copy at http://www.columbia.edu/~sn2294/papers/sng-worldcongress.pdf)

Abstract:

This paper seeks to better understand what makes big data analysis different, what we can and cannot do with existing econometric tools, and what issues need to be dealt with in order to work with the data efficiently.  As a case study, I set out to extract any business cycle information that might exist in four terabytes of weekly scanner data.  The main challenge is to handle the volume, variety, and characteristics of the data within the constraints of our computing environment. Scalable and efficient algorithms are available to ease the computation burden, but they often have unknown statistical properties and are not designed for the purpose of efficient estimation or optimal inference.  As well, economic data have unique characteristics that generic algorithms may not accommodate.  There is a need for computationally efficient econometric methods as big data is likely here to stay.

## Saturday, August 12, 2017

### On Theory, Measurement, and Lewbel's Assertion

Arthur Lewbel, insightful as always, asserts in a recent post that:
The people who argue that machine learning, natural experiments, and randomized controlled trials are replacing structural economic modeling and theory are wronger than wrong.
As ML and experiments uncover ever more previously unknown correlations and connections, the desire to understand these newfound relationships will rise, thereby increasing, not decreasing, the demand for structural economic theory and models.
I agree.  New measurement produces new theory, and new theory produces new measurement -- it's hard to imagine stronger complements.  And as I said in an earlier post,
Measurement and theory are rarely advanced at the same time, by the same team, in the same work. And they don't need to be. Instead we exploit the division of labor, as we should. Measurement can advance significantly with little theory, and theory can advance significantly with little measurement. Still each disciplines the other in the long run, and science advances.
The theory/measurement pendulum tends to swing widely.  If the 1970's and 1980's were a golden age of theory, recent decades have witnessed explosive advances in measurement linked to the explosion of Big Data.  But Big Data presents both measurement opportunities and pitfalls -- dense fogs of "digital exhaust" -- which fresh theory will help us penetrate.  Theory will be back.

[Related earlier posts:  "Big Data the Big Hassle" and "Theory gets too Much Respect, and Measurement Doesn't get Enough"]

## Saturday, August 5, 2017

### 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.

## Sunday, July 30, 2017

### Regression Discontinuity and Event Studies in Time Series

Check out the new paper, "Regression Discontinuity in Time [RDiT]: Considerations for Empirical Applications", by Catherine Hausman and David S. Rapson.  (NBER Working Paper No. 23602, July 2017.  Ungated copy here.)

It's interesting in part because it documents and contributes to the largely cross-section regression discontinuity design literature's awakening to time series. But the elephant in the room is the large time-series "event study" (ES) literature, mentioned but not emphasized by Hausman and Rapson.  [In a one-sentence nutshell, here's how an ES works: model the pre-event period, use the fitted pre-event model to predict the post-event period, and ascribe any systematic forecast error to the causal impact of the event.]  ES's trace to the classic Fama et al. (1969).  Among many others, MacKinlay's 1997 overview is still fresh, and Gürkaynak and Wright (2013) provide additional perspective.

One question is what the RDiT approach adds to the ES approach, and related, what it adds to well-developed time-series toolkit of other methods for assessing structural change. At present, and notwithstanding the Hausman-Rapson paper, my view is "little or nothing".  Indeed in most respects it would seem that a RDiT study *is* an ES, and conversely.  So call it what you will, "ES" or "RDiT"

But there are important open issues in ES / RDiT, and Hausman-Rapson correctly emphasize one of them, namely issues and difficulties associated with "wide" pre- and post-event windows, which is often the relevant case in time series.

Things are generally "easy" in cross sections, where we can usually take narrow windows (e.g., in the classic scholarship exam example, we use only test scores very close to the scholarship threshold).  Things are similarly "easy" in time series *IF* we can take similarly narrow windows (e.g., high-frequency asset return data facilitate taking narrow pre- and post-event windows in financial applications).  In such cases it's comparatively easy to credibly ascribe a post-event break to the causal impact of the event.

But in other time-series areas like macro and environmental, we might want (or need) to use wide pre- and post-event windows.  Then the trick becomes modeling the pre- and post-event periods successfully enough so that we can credibly assert that any structural change is due exclusively to the event -- very challenging, but not hopeless.

Hats off to Hausman and Rapson for beginning to bridge the ES and regression discontinuity literatures, and for implicitly helping to push the ES literature forward.

## Tuesday, July 25, 2017

### Time-Series Regression Discontinuity

I'll have something to say in next week's post.  Meanwhile check out the interesting new paper, "Regression Discontinuity in Time: Considerations for Empirical Applications", by Catherine Hausman and David S. Rapson, NBER Working Paper No. 23602, July 2017.  (Ungated version here.)

## Sunday, July 23, 2017

### 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".

## Thursday, July 13, 2017

### July 12 NBER Discussion Slides

Here are my slides from yesterday.

## Sunday, July 9, 2017

### On the Identification of Network Connectedness

I want to clarify an aspect of the Diebold-Yilmaz framework (e.g., here or here).  It is simply a method for summarizing and visualizing dynamic network connectedness, based on a variance decomposition matrix.  The variance decomposition is not a part of our technology; rather, it is the key input to our technology.  Calculation of a variance decomposition of course requires an identified model.  We have nothing new to say about that; numerous models/identifications have appeared over the years, and it's your choice (but you will of course have to defend your choice).

For certain reasons (e.g., comparatively easy extension to high dimensions) Yilmaz and I generally use a vector-autoregressive model and Koop-Pesaran-Shin "generalized identification".  Again, however, if you don't find that appealing, you can use whatever model and identification scheme you want.  As long as you can supply a credible / defensible variance decomposition matrix, the network summarization / visualization technology can then take over.

## Monday, July 3, 2017

### 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.

## Thursday, June 29, 2017

### More Slides: Forecast Evaluation, DSGE Modeling, and Connectedness

The last post (slides from a recent conference discussion) reminded me of some slide decks that go along with some forthcoming papers.  I hope they're useful.

Diebold, F.X. and Shin, M. (in press), "Assessing Point Forecast Accuracy by Stochastic Error Distance," Econometric Reviews.  Slides here.

Diebold, F.X., Schorfheide, F. and Shin, M. (in press)"Real-Time Forecast Evaluation of DSGE Models with Stochastic Volatility," Journal of Econometrics.  Slides here.

Demirer, M., Diebold, F.X., Liu, L. and Yilmaz, K. (in press), "Estimating Global Bank Network Connectedness", Journal of Applied Econometrics.  Slides here.

## Monday, June 26, 2017

### Slides from SoFiE NYU Discussion

Here are the slides from my pre-conference discussion of Yang Liu's interesting paper, "Government Debt and Risk Premia", at the NYU SoFiE meeting. The key will be to see whether his result (that debt/GDP is a key driver of the equity premium) remains when he controls for expected future real activity. (See Campbell and Diebold, "Stock Returns and Expected Business Conditions: Half a Century of Direct Evidence," Journal of Business and Economic Statistics, 27, 266-278, 2009.)

## Wednesday, June 7, 2017

### Structural Change and Big Data

Recall the tall-wide-dense (T, K, m) Big Data taxonomy.  One might naively assert that tall data (big time dimension, T) are not really a part of the Big Data phenomenon, insofar as T has not started growing more quickly in recent years.  But a more sophisticated perspective on the "size" of T is whether it is big enough to make structural change a potentially serious concern.  And structural change is a serious concern, routinely, in time-series econometrics.  Hence structural change, in a sense, produces Big Data through the T channel.

## Saturday, May 27, 2017

### SoFiE 2017 New York

If you haven't yet been to the Society for Financial Econometrics (SoFiE) annual meeting, now's the time.  They're pulling out all the stops for the 10th anniversary at NYU Stern, June 21-23, 2017.  There will be a good mix of financial econometrics and empirical finance (invited speakers here; full program here). The "pre-conference" will also continue, this year June 20, with presentations by junior scholars (new/recent Ph.D.'s) and discussions by senior scholars. Lots of information here. See you there!

## Monday, May 22, 2017

### Big Data in Econometric Modeling

Here's a speakers' photo from last week's Penn conference, Big Data in Dynamic Predictive Econometric Modeling.  Click through to find the program, copies of papers and slides, a participant list, and a few more photos.  A good and productive time was had by all!

## Monday, May 15, 2017

### 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.

## Monday, May 8, 2017

### Replicating Anomalies

I blogged a few weeks ago on "the file drawer problem".  In that vein, check out the interesting new paper below. I like their term "p-hacking".

Random thought 1:
Note that reverse p-hacking can also occur, when an author wants low p-values.  In the study below, for example, the deck could be stacked with all sorts of dubious/spurious "anomaly variables" that no one ever took seriously.  Then of course a very large number would wind up with low p-values.  I am not suggesting that the study below is guilty of this; rather, I simply had never thought about reverse p-hacking before, and this paper led me to think of the possibility, so I'm relaying the thought.

Related random thought 2:
It would be interesting to compare anomalies published in "top journals" and "non-top journals" to see whether the top journals are more guilty or less guilty of p-hacking.  I can think of competing factors that could tip it either way!

Replicating Anomalies
by Kewei Hou, Chen Xue, Lu Zhang - NBER Working Paper #23394
Abstract:
The anomalies literature is infested with widespread p-hacking. We replicate the entire anomalies literature in finance and accounting by compiling a largest-to-date data library that contains 447 anomaly variables. With microcaps alleviated via New York Stock Exchange breakpoints and value-weighted returns, 286 anomalies (64%) including 95 out of 102 liquidity variables (93%) are insignificant at the conventional 5% level. Imposing the cutoff t-value of three raises the number of insignificance to 380 (85%). Even for the 161 significant anomalies, their magnitudes are often much lower than originally reported. Out of the 161, the q-factor model leaves 115 alphas insignificant (150 with t < 3). In all, capital markets are more efficient than previously recognized.

## Thursday, May 4, 2017

### Network Tools for Understanding High-Dimensional Dynamic Models

The slides from my "overview" IMF talk two weeks ago proved popular, so here are some different overview slides on a different topic ("Estimating and Understanding High-Dimensional Dynamic Stochastic Econometric Models"), from my talk at last week's NYU Stern Conference on Volatility and Derivatives.

## Sunday, April 30, 2017

### One Millionth Birthday...

...in event time.  It's true, yesterday No Hesitations passed 1,000,000 page views.  Totally humbling.  I am grateful for your interest and support.

## Saturday, April 29, 2017

### Predictive Modeling and Causal Estimation

Here are the slides, "Econometrics, Predictive Modeling, and Causal Estimation", from my talk at the recent conference at the IMF in honor of Kajal Lahiri's 70th (group photo above). They build on an earlier No Hesitations post.

## Thursday, April 20, 2017

### Automated Time-Series Forecasting at Google

Check out this piece on automated time-series forecasting at Google.  It's a fun and quick read. Several aspects are noteworthy.

On the upside:

-- Forecast combination features prominently -- they combine forecasts from an ensemble of models.

-- Uncertainty is acknowledged -- they produce interval forecasts, not just point forecasts.

On the downside:

-- There's little to their approach that wasn't well known and widely used in econometrics a quarter century ago (or more).  Might not something like Autobox, which has been around and evolving since the 1970's, do as well or better?

## Friday, April 14, 2017

### On Pseudo Out-of-Sample Model Selection

Great to see that Hirano and Wright (HW), "Forecasting with Model Uncertainty", finally came out in Econometrica. (Ungated working paper version here.)

HW make two key contributions. First, they characterize rigorously the source of the inefficiency in forecast model selection by pseudo out-of-sample methods (expanding-sample, split-sample, ...), adding invaluable precision to more intuitive discussions like Diebold (2015). (Ungated working paper version here.) Second, and very constructively, they show that certain simulation-based estimators (including bagging) can considerably reduce, if not completely eliminate, the inefficiency.

Abstract: We consider forecasting with uncertainty about the choice of predictor variables. The researcher wants to select a model, estimate the parameters, and use the parameter estimates for forecasting. We investigate the distributional properties of a number of different schemes for model choice and parameter estimation, including: in‐sample model selection using the Akaike information criterion; out‐of‐sample model selection; and splitting the data into subsamples for model selection and parameter estimation. Using a weak‐predictor local asymptotic scheme, we provide a representation result that facilitates comparison of the distributional properties of the procedures and their associated forecast risks. This representation isolates the source of inefficiency in some of these procedures. We develop a simulation procedure that improves the accuracy of the out‐of‐sample and split‐sample methods uniformly over the local parameter space. We also examine how bootstrap aggregation (bagging) affects the local asymptotic risk of the estimators and their associated forecasts. Numerically, we find that for many values of the local parameter, the out‐of‐sample and split‐sample schemes perform poorly if implemented in the conventional way. But they perform well, if implemented in conjunction with our risk‐reduction method or bagging.

## Monday, April 10, 2017

### BIg Data, Machine Learning, and the Macroeconomy

Coming soon at Bank of Norway:

CALL FOR PAPERS
Big data, machine learning and the macroeconomy
Norges Bank, Oslo, 2-3 October 2017

Data, in both structured and unstructured form, are becoming easily available on an ever increasing scale. To find patterns and make predictions using such big data, machine learning techniques have proven to be extremely valuable in a wide variety of fields. This conference aims to gather researchers using machine learning and big data to answer challenges relevant for central banking.

Examples of questions, and topics, of interest are:

Forecasting applications and methods
-Can better predictive performance of key economic aggregates (GDP, inflation, etc.) be achieved by using alternative data sources?
- Does the machine learning tool-kit add value to already well-established forecasting frameworks used at central banks?

Causal effects
- How can new sources of data and methods be used learn about the causal mechanism underlying economic fluctuations?

Text as data
- Communication is at the heart of modern central banking. How does this affect markets?
- How can textual data be linked to economic concepts like uncertainty, news, and sentiment?

Confirmed keynote speakers are:
- Victor Chernozhukov (MIT)
- Matt Taddy (Microsoft, Chicago Booth)

The conference will feature 10-12 papers. If you would like to present a paper, please send a draft or an extended abstract to mlconference@norges-bank.no by 31 July 2017. Authors of accepted papers will be notified by 15 August. For other questions regarding this conference, please send an e-mail to mlconference@norges-bank.no. Conference organizers are Vegard H. Larsen and Leif Anders Thorsrud.

### 13th Annual Real-Time Conference

Great news: The Bank of Spain will sponsor the 13th annual conference on real-time data analysis, methods, and applications in macroeconomics and finance, next October 19th and 20th , 2017, in its central headquarters in Madrid, c/ Alcalá, 48.

The real-time conference has always been unique and valuable. I'm very happy to see the Bank of Spain confirming and promoting its continued vitality.

Topics include:

• Nowcasting, forecasting and real-time monitoring of macroeconomic and financial conditions.
• The use of real-time data in policy formulation and analysis.
• New real-time macroeconomic and financial databases.
• Real-time modeling and forecasting aspects of high-frequency financial data.
• Survey data, and its use in macro model analysis and evaluation.
• Evaluation of data revision and real-time forecasts, including point forecasts, probability forecasts, density forecasts, risk assessments and decompositions
.

## Monday, April 3, 2017

### The Latest on the "File Drawer Problem"

The term "file drawer problem" was coined long ago. It refers to the bias in published empirical studies toward "large", or "significant", or "good" estimates. That is, "small"/"insignificant"/"bad" estimates remain unpublished, in file drawers (or, in modern times, on hard drives). Correcting the bias is a tough nut to crack, since little is known about the nature or number of unpublished studies. For the latest, together with references to the relevant earlier literature, see the interesting new NBER working paper, IDENTIFICATION OF AND CORRECTION FOR PUBLICATION BIAS, by Isaiah AndrewsMaximilian Kasy. There's an ungated version and appendix here, and a nice set of slides here.

Abstract: Some empirical results are more likely to be published than others. Such selective publication leads to biased estimators and distorted inference. This paper proposes two approaches for identifying the conditional probability of publication as a function of a study's results, the first based on systematic replication studies and the second based on meta-studies. For known conditional publication probabilities, we propose median-unbiased estimators and associated confidence sets that correct for selective publication. We apply our methods to recent large-scale replication studies in experimental economics and psychology, and to meta-studies of the effects of minimum wages and de-worming programs.

## Tuesday, March 28, 2017

### Text as Data

"Text as data" is a vibrant and by now well-established field. (Just Google "text as data".)

For an informative overview geared toward econometricians, see the new paper, "Text as Data" by Matthew Gentzkow, Bryan T. Kelly, and Matt Taddy (GKT). (Ungated version here.)

"Text as data" has wide applications in economics. As GKT note:

... in finance, text from financial news, social media, and company filings is used to predict asset price movements and study the causal impact of new information. In macroeconomics, text is used to forecast variation in inflation and unemployment, and estimate the effects of policy uncertainty. In media economics, text from news and social media is used to study the drivers and effects of political slant. In industrial organization and marketing, text from advertisements and product reviews is used to study the drivers of consumer decision making. In political economy, text from politicians’ speeches is used to study the dynamics of political agendas and debate.

There are three key steps:

1. Represent the raw text D as a numerical array x

2. Map x into predicted values yhat of outcomes y

3. Use yhat in subsequent descriptive or causal analysis.

GKT emphasize the ultra-high dimensionality inherent in statistical text analyses, with connections to machine learning, etc.

## Tuesday, March 21, 2017

### Forecasting and "As-If" Discounting

Check out the fascinating and creative new paper, "Myopia and Discounting", by Xavier Gabaix and David Laibson.

From their abstract (slightly edited):
We assume that perfectly patient agents estimate the value of future events by generating noisy, unbiased simulations and combining those signals with priors to form posteriors. These posterior expectations exhibit as-if discounting: agents make choices as if they were maximizing a stream of known utils weighted by a discount function. This as-if discount function reflects the fact that estimated utils are a combination of signals and priors, so average expectations are optimally shaded toward the mean of the prior distribution, generating behavior that partially mimics the properties of classical time preferences. When the simulation noise has variance that is linear in the event's horizon, the as-if discount function is hyperbolic.
Among other things, then, they provide a rational foundation for the "myopia" associated with hyperbolic discounting.

Note that in the Gabaix-Laibson environment everything depends on how forecast error variance behaves as a function of forecast horizon $$h$$. But we know a lot about that. For example, in linear covariance-stationary $$I(0)$$ environments, optimal forecast error variance grows with $$h$$ at a decreasing rate, approaching the unconditional variance from below. Hence it cannot grow linearly with $$h$$, which is what produces hyperbolic as-if discounting. In contrast, in non-stationary $$I(1)$$ environments, optimal forecast error variance does eventually grow linearly with $$h$$. In a random walk, for example, $$h$$-step-ahead optimal forecast error variance is just $$h \sigma^2$$, where $$\sigma^2$$ is the innovation variance. It would be fascinating to put people in $$I(1)$$ vs. $$I(0)$$ laboratory environments and see if hyperbolic as-if discounting arises in $$I(1)$$ cases but not in $$I(0)$$ cases.

## Sunday, March 19, 2017

### ML and Metrics VIII: The New Predictive Econometric Modeling

[Click on "Machine Learning" at right for earlier "Machine Learning and Econometrics" posts.]

We econometricians need -- and have always had -- cross section and time series ("micro econometrics" and "macro/financial econometrics"), causal estimation and predictive modeling, structural and non-structural. And all continue to thrive.

But there's a new twist, happening now, making this an unusually exciting time in econometrics. P
redictive econometric modeling is not only alive and well, but also blossoming anew, this time at the interface of micro-econometrics and machine learning. A fine example is the new Kleinberg, Lakkaraju, Leskovic, Ludwig and Mullainathan paper, “Human Decisions and Machine Predictions”, NBER Working Paper 23180 (February 2017).

Good predictions promote good decisions, and econometrics is ultimately about helping people to make good decisions. Hence the new developments, driven by advances in machine learning, are most welcome contributions to a long and distinguished predictive econometric modeling tradition.

## Monday, March 13, 2017

### ML and Metrics VII: Cross-Section Non-Linearities

[Click on "Machine Learning" at right for earlier "Machine Learning and Econometrics" posts.]

The predictive modeling perspective needs not only to be respected and embraced in econometrics (as it routinely is, notwithstanding the Angrist-Pischke revisionist agenda), but also to be enhanced by incorporating elements of statistical machine learning (ML). This is particularly true for cross-section econometrics insofar as time-series econometrics is already well ahead in that regard.  For example, although flexible non-parametric ML approaches to estimating conditional-mean functions don't add much to time-series econometrics, they may add lots to cross-section econometric regression and classification analyses, where conditional mean functions may be highly nonlinear for a variety of reasons.  Of course econometricians are well aware of traditional non-parametric issues/approaches, especially kernel and series methods, and they have made many contributions, but there's still much more to be learned from ML.

## Monday, March 6, 2017

### ML and Metrics VI: A Key Difference Between ML and TS Econometrics

[Click on "Machine Learning" at right for earlier "Machine Learning and Econometrics" posts.]

Continuing:

So then, statistical machine learning (ML) and
time series econometrics (TS) have lots in common. But there's also an interesting difference: ML's emphasis on flexible nonparametric modeling of conditional-mean nonlinearity doesn't play a big role in TS.

Of course there are the traditional TS conditional-mean nonlinearities: smooth non-linear trends, seasonal shifts, and so on. But there's very little evidence of important conditional-mean nonlinearity in the covariance-stationary (de-trended, de-seasonalized) dynamics of most economic time series. Not that people haven't tried hard -- really hard -- to find it, with nearest neighbors, neural nets, random forests, and lots more.

So it's no accident that things like linear autoregressions remain overwhelmingly dominant in TS. Indeed I can think of only one type of conditional-mean nonlinearity that has emerged as repeatedly important for (at least some) economic time series: Hamilton-style Markov-switching dynamics.

[Of course there's a non-linear elephant in the room:  Engle-style GARCH-type dynamics. They're tremendously important in financial econometrics, and sometimes also in macro-econometrics, but they're about conditional variances, not conditional means.]

So there are basically only two important non-linear models in TS, and only one of them speaks to conditional-mean dynamics. And crucially, they're both very tightly parametric, closely tailored to specialized features of economic and financial data.

Now let's step back and assemble things:

ML emphasizes approximating non-linear conditional-mean functions in highly-flexible non-parametric fashion. That turns out to be doubly unnecessary in TS: There's just not much conditional-mean non-linearity to worry about, and when there occasionally is, it's typically of a highly-specialized nature best approximated in highly-specialized (tightly-parametric) fashion.

## Sunday, February 26, 2017

### Machine Learning and Econometrics V: Similarities to Time Series

[Notice that I changed the title from "Machine Learning vs. Econometrics" to "Machine Learning and  Econometrics", as the two are complements, not competitors, as this post will begin to emphasize. But I've kept the numbering, so this is number five.  For others click on Machine Learning at right.]

Thanks for the overwhelming response to my last post, on Angrist-Pischke (AP).  I'll have more to say on AP a few posts from now, but first I need to set the stage.

A key observation is that statistical machine learning (ML) and time-series econometrics/statistics (TS) are largely about modeling, and they largely have the same foundational perspective. Some of the key ingredients are:

-- George Box got it right: "All models are false; some are useful", so search for good approximating models, not "truth".

-- Be explicit about the loss function, that is, about what defines a "good approximating model" (e.g., 1-step-ahead out-of-sample mean-squared forecast error)

-- Respect and optimize that loss function in model selection (e.g., BIC)

-- Respect and optimize that loss function in estimation (e.g., least squares)

-- Respect and optimize that loss function in forecast construction (e.g., Wiener-Kolmogorov-Kalman)

-- Respect and optimize that loss function in forecast evaluation, comparison, and combination (e.g., Mincer-Zarnowitz evaluations, Diebold-Mariano comparisons, Granger-Ramanathan combinations).

So time-series econometrics should embrace ML -- and it is.  Just look at recent work like this.

## Sunday, February 19, 2017

### Econometrics: Angrist and Pischke are at it Again

Check out the new Angrist-Pischke (AP), "Undergraduate Econometrics Instruction: Through Our Classes, Darkly".

I guess I have no choice but to weigh in. The issues are important, and my earlier AP post, "Mostly Harmless Econometrics?", is my all-time most popular.

Basically AP want all econometrics texts to look a lot more like theirs. But their books and their new essay unfortunately miss (read: dismiss) half of econometrics.

Here's what AP get right:

(Goal G1) One of the major goals in econometrics is predicting the effects of exogenous "treatments" or "interventions" or "policies". Phrased in the language of estimation, the question is "If I intervene and give someone a certain treatment $${\partial x}, x \in X$$, what is my minimum-MSE estimate of her $$\ \partial y$$?" So we are estimating the partial derivative $${\partial y / \partial x}$$.

AP argue the virtues and trumpet the successes of a "design-based" approach to G1. In my view they make many good points as regards G1: discontinuity designs, dif-in-dif designs, and other clever modern approaches for approximating random experiments indeed take us far beyond "Stones'-age" approaches to G1.
(AP sure turn a great phrase...). And the econometric simplicity of the design-based approach is intoxicating: it's mostly just linear regression of $$y$$ on $$x$$ and a few cleverly-chosen control variables -- you don't need a full model -- with White-washed standard errors. Nice work if you can get it. And yes, moving forward, any good text should feature a solid chapter on those methods.

Here's what AP miss/dismiss:

(Goal G2) The other major goal in econometrics is predicting $$y$$. In the language of estimation, the question is "If a new person $$i$$ arrives with covariates $$X_i$$, what is my minimum-MSE estimate of her $$y_i$$? So we are estimating a conditional mean $$E(y | X)$$, which in general is very different from estimating a partial derivative $${\partial y / \partial x}$$.

The problem with the AP paradigm is that it doesn't work for goal G2. Modeling nonlinear functional form is important, as the conditional mean function $$E(y | X)$$ may be highly nonlinear in $$X$$; systematic model selection is important, as it's not clear a priori what subset of $$X$$ (i.e., what model) might be most useful for approximating $$E(y | X)$$; detecting and modeling heteroskedasticity is important (in both cross sections and time series), as it's the key to accurate interval and density prediction; detecting and modeling serial correlation is crucially important in time-series contexts, as "the past" is the key conditioning information for predicting "the future"; etc., etc, ...

(Notice how often "model" and "modeling" appear in the above paragraph. That's precisely what AP dismiss, even in their abstract, which very precisely, and incorrectly, declares that "Applied econometrics ...[now prioritizes]... the estimation of specific causal effects and empirical policy analysis over general models of outcome determination".)

The AP approach to goal G2 is to ignore it, in a thinly-veiled attempt to equate econometrics exclusively with G1, which nicely feathers the AP nest. Sorry guys, but no one's buying it. That's why the textbooks continue to feature G2 tools and techniques so prominently, as well they should.

## Monday, February 13, 2017

### Predictive Loss vs. Predictive Regret

It's interesting  to contrast two prediction paradigms.

A.  The universal statistical/econometric approach to prediction:
Take a stand on a loss function and find/use a predictor that minimizes conditionally expected loss.  Note that this is an absolute standard.  We minimize loss, not some sort of relative loss.

B.  An alternative approach to prediction, common in certain communities/literatures:
Take a stand on a loss function and find/use a predictor that minimizes regret.  Note that this is a relative standard.  Regret minimization is relative loss minimization, i.e., striving to do no worse than others.

Approach A strikes me as natural and appropriate, whereas B strikes me as as quirky and "behavioral".  That is, it seems to me that we generally want tools that perform well, not tools that merely perform no worse than others.

There's also another issue, the ex ante nature of A (standing in the present, conditioning on available information, looking forward) vs. the ex post nature of B (standing in the future, looking backward).  Approach A again seems more natural and appropriate.

## Sunday, February 5, 2017

### Data for the People

Data for the People, by Andreas Weigend, is coming out this week, or maybe it came out last week. Andreas is a leading technologist (at least that's the most accurate one-word description I can think of), and I have valued his insights ever since we were colleagues at NYU almost twenty years ago. Since then he's moved on to many other things; see http://www.weigend.com

Andreas challenges prevailing views about data creation and "data privacy". Rather than perpetuating a romanticized view of data privacy, he argues that we need increased data transparency, combined with increased data literacy, so that people can take command of their own data. Drawing on his work with numerous firms, he proposes six "data rights":

-- The right to access data
-- The right to amend data
-- The right to blur data
-- The right to port data
-- The right to inspect data refineries
-- The right to experiment with data refineries

Check out Data for the People at http://ourdata.com.

[Acknowledgment: Parts of this post were adapted from the book's web site.]

## Monday, January 30, 2017

### Randomization Tests for Regime Switching

I have always been fascinated by distribution-free non-parametric tests, or randomization tests, or Monte Carlo tests -- whatever you want to call them.  (For example, I used some in ancient work like Diebold-Rudebusch 1992.)  They seem almost too good to be true: exact finite-sample tests without distributional assumptions!  They also still seem curiously underutilized in econometrics, notwithstanding, for example, the path-breaking and well-known contributions over many decades by Jean-Marie Dufour, Marc Hallin, and others.

For the latest, see the fascinating new contribution by Jean-Marie Dufour and Richard Luger. They show how to use randomization to perform simple tests of the null of linearity against the alternative of Markov switching in dynamic environments.  That's a very hard problem (nuisance parameters not identified under the null, singular information matrix under the null), and several top researchers have wrestled with it (e.g., GarciaHansen, Carasco-Hu-Ploberger). Randomization delivers tests that are exact, distribution-free, and simple. And power looks pretty good too.

## Monday, January 23, 2017

### Bayes Stifling Creativity?

Some twenty years ago, a leading Bayesian econometrician startled me during an office visit at Penn. We were discussing Bayesian vs. frequentist approaches to a few things, when all of a sudden he declared that "There must be something about Bayesian analysis that stifles creativity.  It seems that frequentists invent all the great stuff, and Bayesians just trail behind, telling them how to do it right".

His characterization rings true in certain significant respects, which is why it's so funny.  But the intellectually interesting thing is that it doesn't have to be that way.  As Chris Sims notes in a recent communication:
... frequentists are in the habit of inventing easily computed, intuitively appealing estimators and then deriving their properties without insisting that the method whose properties they derive is optimal.  ... Bayesians are more likely to go from model to optimal inference, [but] they don't have to, and [they] ought to work more on Bayesian analysis of methods based on conveniently calculated statistics.

See Chris' thought-provoking unpublished paper draft, "Understanding Non-Bayesians".

[As noted on Chris' web site, he wrote that paper for the Oxford University Press Handbook of Bayesian Econometrics, but he "withheld [it] from publication there because of the Draconian copyright agreement that OUP insisted on --- forbidding posting even a late draft like this one on a personal web site."]

## Monday, January 16, 2017

### Impulse Responses From Smooth Local Projections

Check out Barnichon-Brownlees (2017) (BB).  As proposed and developed in Jorda (2005), they estimate impulse-response functions (IRF's) directly by projecting outcomes on estimates of structural shocks at various horizons, as opposed to inverting a fitted autoregression.  The BB enhancement relative to Jorda is the effective incorporation of a smoothness prior in IRF estimation.  (Notice that the traditional approach of inverting a low-ordered autoregression automatically promotes IRF smoothness.)  In my view, smoothness is a natural IRF shrinkage direction, and BB convincingly show that it's likely to enhance estimation efficiency relative to Jorda's original approach. I always liked the idea of attempting to go after IRF's directly, and Jorda/BB seems appealing.

## Friday, January 13, 2017

### Math Rendering Problem Fixed

The problem with math rendering in the recent post, "All of Machine Learning in One Expression", is now fixed (I hope).  That is, the math should now look like math, not LaTeX code, on all devices.

## Monday, January 9, 2017

### All of Machine Learning in One Expression

Sendhil Mullainathan gave an entertaining plenary talk on machine learning (ML) in finance, in Chicago last Saturday at the annual American Finance Association (AFA) meeting. (Many hundreds of people, standing room only -- great to see.) Not much new relative to the posts here, for example, but he wasn't trying to deliver new results. Rather he was trying to introduce mainstream AFA financial economists to the ML perspective.

[Of course ML perspective and methods have featured prominently in time-series econometrics for many decades, but many of the recent econometric converts to ML (and audience members at the AFA talk) are cross-section types, not used to thinking much about things like out-of-sample predictive accuracy, etc.]

Anyway, one cute and memorable thing -- good for teaching -- was Sendhil's suggestion that one can use the canonical penalized estimation problem as a taxonomy for much of ML.  Here's my quick attempt at fleshing out that suggestion.

Consider estimating a parameter vector $$\theta$$ by solving the penalized estimation problem,

$$\hat{\theta} = argmin_{\theta} \sum_{i} L (y_i - f(x_i, \theta) ) ~~s.t.~~ \gamma(\theta) \le c ,$$

or equivalently in Lagrange multiplier form,

$$\hat{\theta} = argmin_{\theta} \sum_{i} L (y_i - f(x_i, \theta) ) + \lambda \gamma(\theta) .$$

Then:

(1) $$f(x_i, \theta)$$ is about the modeling strategy (linear, parametric non-linear, non-parametric non-linear (series, trees, nearest-neighbor, kernel, ...)).

(2) $$\gamma(\theta)$$ is about the type of regularization. (Concave penalty functions non-differentiable at the origin produce selection to zero, smooth convex penalties produce shrinkage toward 0, the LASSO penalty is both concave and convex, so it both selects and shrinks, ...)

(3) $$\lambda$$ is about the strength of regularization.

(4) $$L(y_i - f(x_i, \theta) )$$ is about predictive loss (quadratic, absolute, asymmetric, ...).

Many ML schemes emerge as special cases. To take just one well-known example, linear regression with regularization by LASSO and regularization strength chosen to optimize out-of-sample predictive MSE corresponds to (1) $$f(x_i, \theta)$$ linear, (2) $$\gamma(\theta) = \sum_j |\theta_j|$$, (3) $$\lambda$$ cross-validated, and (4) $$L(y_i - f(x_i, \theta) ) = (y_i - f(x_i, \theta) )^2$$.

## Tuesday, January 3, 2017

### Torpedoing Econometric Randomized Controlled Trials

A very Happy New Year to all!

I get no pleasure from torpedoing anything, and "torpedoing" is likely exaggerated, but nevertheless take a look at "A Torpedo Aimed Straight at HMS Randomista". It argues that many econometric randomized controlled trials (RCT's) are seriously flawed -- not even internally valid -- due to their failure to use double-blind randomization. At first the non-double-blind critique may sound cheap and obvious, inviting you to roll your eyes and say "get over it". But ultimately it's not.

Note the interesting situation. Everyone these days is worried about external validity (extensibility), under the implicit assumption that internal validity has been achieved (e.g., see this earlier post). But the
non-double-blind critique makes clear that even internal validity may be dubious in econometric RCT's as typically implemented.

The underlying research paper, "Behavioural Responses and the Impact of New Agricultural Technologies: Evidence from a Double-Blind Field Experiment in Tanzania", by Bulte et al., was published in 2014 in the American Journal of Agricultural Economics. Quite an eye-opener
.

Here's the abstract:

Randomized controlled trials in the social sciences are typically not double-blind, so participants know they are “treated” and will adjust their behavior accordingly. Such effort responses complicate the assessment of impact. To gauge the potential magnitude of effort responses we implement an open RCT and double-blind trial in rural Tanzania, and randomly allocate modern and traditional cowpea seed-varieties to a sample of farmers. Effort responses can be quantitatively important––for our case they explain the entire “treatment effect on the treated” as measured in a conventional economic RCT. Specifically, harvests are the same for people who know they received the modern seeds and for people who did not know what type of seeds they got, but people who knew they received the traditional seeds did much worse. We also find that most of the behavioral response is unobserved by the analyst, or at least not readily captured using coarse, standard controls.