Unbiased Model Selection Using the Adjusted R-Squared

The coefficient of determination (R²), and its "adjusted" counterpart, really don't impress me much! I often tell students that this statistic is one of the last things I look at when appraising the results of estimating a regression model.

Previously, I've had a few things to say about this measure of goodness-of-fit  (e.g., here and here). In this post I want to say something positive, for once, about "adjusted" R². Specifically, I'm going to talk about its use as a model-selection criterion.

This Job is Killing Me!

The Indeed website (available for a number of countries) is a well-known clearing house for jobs and job-seekers.Trolling for opportunities there earlier today, I decided to take a peek at trends in job postings relating to econometrics and the funeral business. (At my age, such associations come easily!)

So, based on data for just the U.S., here is what I found. First, I looked at the number of posted jobs (as a percentage of all postings). The trends since the beginning of 2011 are interesting!

Next, I looked at the % growth rates in the job postings since 2005:

Perhaps a cointegration analysis would be in order!

© 2013, David E. Giles

Allocation Models With Autocorrelated Errors

Not too long ago, I had a couple of posts about "allocation models" (here and here). These models are systems of regression equations in which there is a constraint on the data for the dependent variables for the equations. Specifically, at every point in the sample, these variables sum exactly to the value of a linear combination of the regressors. In practice, this linear combination usually is very simple - it's just one of the regressors.

So, for example, suppose that the dependent variables measure the shares of Canada's exports that go to different countries. These shares must add up to one in value. If we have an intercept (a series of "ones") in each equation, then we have an allocation model.

In one of the comments on the earlier posts, I was asked about the possibility of autocorrelated errors in the empirical example that I provided. In my response, I noted that if autocorrelation is present, and is allowed for in the estimation of the model, then special care is needed. In particular, any modification to the model, to allow for a specific form of autocorrelation, must satisfy the "adding up" constraints that are fundamental to the allocation model.

Let's see what this involves, in practice.

Some Recent, and Transparently Applicable, Results in Time-Series Econometrics

I think most of us would agree that when new techniques are introduced in econometrics, it's often a bit of a challenge to see exactly what would be involved in applying them. Someone comes up with a new estimator or test, and it's often a while before it gets incorporated into our favourite econometrics package, or until someone puts together an expository piece that illustrates, in simple terms, how to put the theory into practice.

In part, that's why applied econometrics "lags behind" econometric theory. Another reason is that a lot of practitioners aren't interested in reading the latest theoretical paper themselves.

Fair enough!

In any event, it's always refreshing when new inferential procedures are introduced into the literature in a way that exhibits a decent degree of "transparency" with respect to their actual application. For those of you who like you keep up with recent developments in time-series econometrics, here are some good examples of recent papers that (in my view) score well on the "transparency index":

Francis Diebold on GMM

On his blog, No Hesitations, Francis Diebold has two recent posts about GMM estimation that students of econometrics, and practitioners, definitely should read.

The first of these posts is here, and the second follow-up post is here.

Enjoy!

© 2013, David E. Giles

Recent, and Recommended.......

Recently, I griped posted about the need to get the economics back into papers that the authors characterize as "microeconometrics". Although I was venting (just a little!) about the "disconnect" that we so often see, between the theory section and the empirical section, in so many of the papers in this category, I also commented that there are plenty of papers out there that avoid this disconnect. I just wish there were more of them!

In response to one of the comments of that post, I gave just one such example, and afterwards I thought that although my choice was a good one, it was somewhat dated. So, on a more positive note, what about some recent papers that exemplify what I'm looking for, and what I'd like to see more of?

Information Criteria Unveiled

Most of you will have used, or at least encountered, various "information criteria" when estimating a regression model, an ARIMA model, or a VAR model. These criteria provide us with a way of comparing alternative model specifications, and selecting between them. 

They're not test statistics. Rather, they're minus twice the maximized value of the underlying log-likelihood function, adjusted by a "penalty factor" that depends on the number of parameters being estimated. The more parameters, the more complicated is the model, and the greater the penalty factor. For a given level of "fit", a more parsimonious model is rewarded more than a more complex model. Changing the exact form of the penalty factor gives rise to a different information criterion.

However, did you ever stop to ask "why are these called information criteria?" Did you realize that these criteria - which are, after all, statistics - have different properties when it comes to the probability that they will select the correct model specification? In this respect, they are typically biased, and some of them are even inconsistent.

This sounds like something that's worth knowing more about!

Former Students

It's always great to catch up with former students. I guess this is especially true of grad. students because (inevitably) you get to spend a lot of one-on-one time with them, and get to know them pretty well.

So, today I was thrilled to meet up with not one, but three, former grad. students! Peter Jacobsen, Cameron Woodbridge, and William Bi are all working for the B.C. Ministry of Forests, Lands and Natural Resource Operations, here in Victoria. I've known them all for quite some time. In fact, Peter was only the second M.A. student I supervised after I moved to UVic in 1994. 

Great lunch, guys!

© 203, David E. Giles

Some Current Projects

I often get emails asking me what research projects I'm working on. Generally, I have several projects underway at any given time - usually at various stages of development or completion. In that respect I guess I'm pretty typical.

I also tend to have a mixture of theoretical and applied projects, some econometric and some essentially statistical in nature. I find that this provides some continuity in my work. It's not easy to focus on just one or two research projects all of the time, especially if they're not progressing as well as you'd like them to!

So, what am I up to right now? Here are some of the papers/projects that I'm working on:

Vintage Years in Econometrics - The 1950's

Following on from my earlier posts about vintage years for econometrics in the 1930's and 1940's, here's my run-down on the 1950's.

As before, let me note that "in econometrics, what constitutes quality and importance is partly a matter of taste - just like wine! So, not all of you will agree with the choices I've made in the following compilation."