Panel GLS w Arbitrary Cov Matrices

Check out the fine new paper, "Feasible Generalized Least Squares for Panel Data with
Cross-sectional and Serial Correlations," by Jushan Bai, Sung Hoon Choi, and Yuan Liao.

Really nice feasible GLS (yes, GLS!) panel regression allowing for general disturbance heteroskedasticity, serial correlation, and/or spatial correlation.

It's an interesting move back to efficient GLS estimation instead of punting on efficiency and just White-washing s.e.'s with a HAC estimator, which I always found rather unsettling. (See here and here.)  The cool twist is that Bai et al. allow for very general disturbance covariance structures, just as with HAC, without giving away efficiency since they do GLS. The best of both worlds!

So nice to have one of the paper's authors, Yuan Liao, visiting Penn Economics this year. What a windfall for us.

Inference with Social Network Dependence

I'm running behind as usual. I meant to post this right after the seminar, about two weeks ago.  Really interesting stuff -- spatial correlation due to network dependence.  A Google search will find the associated paper(s) instantly. Again, really good stuff.  BUT I would humbly suggest that the biostat people need to read more econometrics. A good start is this survey (itself four years old, and distilled for practitioners as the basic insights were known/published decades ago). The cool question moving forward is whether/when/how network structure can be used to determine/inform clustering.

Elizabeth L. Ogburn

Department of Biostatistics

Johns Hopkins University

Social Network dependence,

the replication crisis, and (in)valid inference

                                                               ABSTRACT

In the first part of this talk, I will show that social network structure can result in a new kind of structural confounding, confounding by network structure, potentially contributing to replication crises across the health and social sciences.  Researchers in these fields frequently sample subjects from one or a small number of communities, schools, hospitals, etc., and while many of the limitations of such convenience samples are well-known, the issue of statistical dependence due to social network ties has not previously been addressed. A paradigmatic example of this is the Framingham Heart Study (FHS). Using a statistic that we adapted to measure network dependence, we test for network dependence and for possible confounding by network structure in several of the thousands of influential papers published using FHS data. Results suggest that some of the many decades of research on coronary heart disease, other health outcomes, and peer influence using FHS data may be biased (away from the null) and anticonservative due to unacknowledged network structure.

But data with network dependence abounds, and in many settings researchers are explicitly interested in learning about social network dynamics.  Therefore, there is high demand for methods for causal and statistical inference with social network data. In the second part of the talk, I will describe recent work on causal inference for observational data from a single social network, focusing on (1) new types of causal estimands that are of interest in social network settings, and (2) conditions under which central limit theorems hold and inference based on approximate normality is licensed.

The HAC Emperor has no Clothes: Part 2

The time-series kernel-HAC literature seems to have forgotten about pre-whitening. But most of the action is in the pre-whitening, as stressed in my earlier post. In time-series contexts, parametric allowance for good-old ARMA-GARCH disturbances (with AIC order selection, say) is likely to be all that's needed, cleaning out whatever conditional-mean and conditional-variance dynamics are operative, after which there's little/no need for anything else. (And although I say "parametric" ARMA/GARCH, it's actually fully non-parametric from a sieve perspective.)

Instead, people focus on kernel-HAC sans prewhitening, and obsess over truncation lag selection. Truncation lag selection is indeed very important when pre-whitening is forgotten, as too short a lag can lead to seriously distorted inference, as emphasized in the brilliant early work of Kiefer-Vogelsang and in important recent work by Lewis, Lazarus, Stock and Watson. But all of that becomes much less important when pre-whitening is successfully implemented.

[Of course spectra need not be rational, so ARMA is just an approximation to a more general Wold representation (and remember, GARCH(1,1) is just an ARMA(1,1) in squares). But is that really a problem? In econometrics don't we feel comfortable with ARMA approximations 99.9 percent of the time? The only econometrically-interesting process I can think of that doesn't admit a finite-ordered ARMA representation is long memory (fractional integration). But that too can be handled parametrically by introducing just one more parameter, moving from ARMA(p,q) to ARFIMA(p,d,q).]

My earlier post linked to the key early work of Den Haan and Levin, which remains unpublished. I am confident that their basic message remains intact. Indeed recent work revisits and amplifies it in important ways; see Kapetanios and Psaradakis (2016) and new work in progress by Richard Baillie to be presented at the September 2016 NBER/NSF time-series meeting at Columbia ("Is Robust Inference with OLS Sensible in Time Series Regressions?").

Endogeneity-Robust OLS Estimation (?)

Imagine White-style robust OLS inference, but with robustness to endogeneity as opposed to heteroskedasticity/autocorrelation (or maybe even robustness to all three).  It sounds too good to be true.  Actually, it sounds impossible, and even if somehow possible, it would of course require not only post-OLS tweaking of standard errors but also post-OLS tweaking of coefficient estimates.  But there are actually some emerging results – embryonic and requiring strict conditions -- but results nonetheless.  Quite intriguing.  Check out Jan Kiviet’s latest paper, "When is it Really Justifiable to Ignore Explanatory Variable Endogeneity in a Regression Model?"

The HAC Emperor has no Clothes

Well, at least in time-series settings. (I'll save cross sections for a later post.)

Consider a time-series regression with possibly heteroskedastic and/or autocorrelated disturbances, 

\( y_t = x_t' \beta + \varepsilon_t  \). 

A popular approach is to punt on the potentially non-iid disturbance, instead simply running OLS with kernel-based heteroskedasticity and autocorrelation consistent (HAC) standard errors.

Punting via kernel-HAC estimation is a bad idea in time series, for several reasons:

(1) [Kernel-HAC is not likely to produce good \(\beta\) estimates.] It stays with OLS and hence gives up on efficient estimation of \(\hat{\beta}\). In huge samples the efficiency loss from using OLS rather than GLS/ML is likely negligible, but time-series samples are often smallish. For example, samples like 1960Q1-2014Q4 are typical in macroeconomics -- just a couple hundred observations of highly-serially-correlated data.

(2) [Kernel-HAC is not likely to produce good \(\beta\) inference.] Its standard errors are not tailored to a specific parametric approximation to \(\varepsilon\) dynamics. Proponents will quickly counter that that's a benefit, not a cost, and in some settings the proponents may be correct. But not in time series settings. In time series, \(\varepsilon\) dynamics are almost always accurately and parsimoniously approximated parametrically (ARMA for conditional mean dynamics in \(\varepsilon\), and GARCH for conditional variance dynamics in \(\varepsilon\)). Hence kernel-HAC standard errors may be unnecessarily unreliable in small samples, even if they're accurate asymptotically. And again, time-series sample sizes are often smallish. 

(3) [Most crucially, kernel-HAC fails to capture invaluable predictive information.] Time series econometrics is intimately concerned with prediction, and explicit parametric modeling of dynamic heteroskedasticity and autocorrelation in \(\varepsilon\) can be used for improved prediction of \(y\). Autocorrelation can be exploited for improved point prediction, and dynamic conditional heteroskedasticity can be exploited for improved interval and density prediction. Punt on them and you're potentially leaving a huge amount of money on the table.

The clearly preferable approach is traditional parametric disturbance heteroskedasticty / autocorrelation modeling, with GLS/ML estimation. Simply allow for ARMA(p,q)-GARCH(P,Q) disturbances (say), with p,q, P and Q selected by AIC (say). (In many applications something like AR(3)-GARCH(1,1) or ARMA(1,1)-GARCH(1,1) would be more than adequate.) Note that the traditional approach is actually fully non-parametric when appropriately viewed as a sieve, and moreover it features automatic bandwidth selection.

Kernel-HAC people call the traditional strategy "pre-whitening," to be done prior to kernel-HAC estimation. But the real point is that it's all -- or at least mostly all -- in the pre-whitening.

In closing, I might add that the view expressed here is strongly supported by top-flight research. On my point (2) and my general recommendation, for example, see the insightful work of den Haan and Levin (2000). It fell on curiously deaf ears and remains unpublished many years later. (It's on Wouter den Haan's web site in a section called "Sleeping and Hard to Get"!) In the interim much of the world jumped on the kernel-HAC bandwagon. It's time to jump off.