Mark Thoma in "The Browser"

It was nice to see this interview with Mark Thoma in The Browser today.

Enjoy!

© 2012, David E. Giles

The Milliken-Graybill Theorem

Let's think about a standard result from regression analysis that we're totally familiar with. Suppose that we have a linear OLS regression model with non-random regressors, and normally distributed errors that are serially independent and homoskedastic. Then, the usual F-test statistic, for testing the validity of a set of linear restrictions on the model's parameters, is exactly  F-distributed in finite samples, if the null hypothesis is true.

In fact, the F-test is Uniformly Most Powerful Invariant (UMPI) in this situation. That's why we use it! If the null hypothesis is false, then this test statistic follows a non-central F-distribution.

It's less well-known that all of these results still hold if the assumed normality of the errors is dropped in favour of an assumption that the errors follow any distribution in the so-called "elliptically symmetric" family of distributions. On this point, see my earlier post here.

What if I were now to say that some of the regressors are actually random, rather than non-random? Is the F-test statistic still exactly F-distributed (under the null hypothesis)?

The Role of Statistics in the Higgs Boson Discovery

With the scientific world abuzz today over the (possible) confirmation of the existence of the Higgs Boson, this post from David Smith on the SmartData Collective is a must-read for anyone with an interest in statistics.

© 2012, David E. Giles

SURE Models

In recent weeks I've had several people email to ask if I can recommend a book that goes into all of the details about the "Seemingly Unrelated Regression Equations" (SURE, or just SUR) model.

Any decent econometrics text discusses this model, of course. However, the treatment usually focuses on the asymptotic properties of the standard estimators - iterated feasible GLS, or MLE.

Attention, Stata Users

I've mentioned the Econometrics by Simulation blog before. Although it's still relatively new, it's had some great posts, and Francis Smart is doing a terrific job, as is reflected in the way that the page view numbers are building up.

Definitely worth a look, especially (but not only) if you're a Stata user.

© 2012, David E. Giles

F-tests Based on the HC or HAC Covariance Matrix Estimators

We all do it - we compute "robust" standard errors when estimating a regression model in any context where we suspect that the model's errors may be heteroskedastic and/or autocorrelated.

More correctly, we select the option in our favourite econometrics package so that the (asymptotic) covariance matrix for our estimated coefficients is estimated, using either White's heteroskedasticity-consistent (HC) estimator, or the Newey-West heteroskedasticity & autocorrelation-consistent (HAC) estimator.

The square roots of the diagonal elements of the estimated covariance matrix then provide us with the robust standard errors that we want. These standard errors are consistent estimates of the true standard deviations of the estimated coefficients, even if the errors are heteroskedastic (in White's case) or heteroskedastic and/or autocorrelated (in the Newey-West case).

That's fine, as long as we keep in mind that this is just an asymptotic result.

Then, we use the robust standard error to construct a "t-test"; or the estimated covariance matrix to construct an "F-test", or a Wald test.

And that's when the trouble starts!

Highly Cited Statistical Papers for Econometricians

There are "classic" research papers in all disciplines. As econometricians we frequently find ourselves making reference to publications by authors who are statisticians. Have you ever wondered how the statistical papers that are important to us actually "stack up" when it comes to a more general audience?

Specifically, how widely cited are these statistical  papers?

Fixed-Effects Vector Decomposition

Warning! Avoid the so-called "Fixed-Effects Vector Decomposition" (FEVD) estimator, introduced by Plümper and Troeger in a 2007 issue of Political Analysis.

A recent "Symposium on Fixed-Effects Vector Decomposition" in the 2011 volume of that journal, which included critiques by William Greene and by Trevor Breusch et al.,  reveals just what this estimator is.... and isn't!

Integrated & Cointegrated Data

Last week I had a post titled More About Spurious Regressions. Implicitly, in that post, I assumed that readers would be familiar with terms such as "integrated data", "cointegration", "differencing", and "error correction model".

It tuns out that my assumption was wrong, as was apparent from the comment/request left  on that post by one of my favourite readers (Anonymous), who wrote:

"The headlined subject of this post is of great interest to me -- a non-specialist. But this communication suffers greatly from the absence of a single real-world example of, e.g. "integrated" or "co-integrated" data, "differencing" (?), "error-correction model," etc. etc. 

I'm not trying to be querulous. It's just that not all your interested readers are specialists. And the extra intellectual effort required to provide examples would help us..."

Monte Carlo Experiments With gretl

I keep saying that I must make more use of the gretl econometrics package. It's great software, and it's free! So, shame on me for not putting my effort where my mouth is.

Fortunately, Riccardo (Jack) Lucchetti keeps a bit of an eye on me in this regard!