Large and Small Regression Coefficients

Here's a trap that newbies to regression analysis have been known to fall into. It's to do with comparing the numerical values of the point estimates of  regression coefficients, and drawing conclusions that may not actually be justified.

What I have in mind is the following sort of situation. Suppose that Betsy (name changed to protect the innocent) has estimated a regression model that looks like this:

               Y = 0.4 + 3.0X₁ - 0.7X₂ + 6.0X₃ +.....+ residual .

Betsy is really proud of her first OLS regression, and tells her friends that "X3 is two times more important  in explaining y than is X1" (or words to that effect).

Putting to one side such issues as statistical significance (I haven't reported any standard errors for the estimated coefficients), Is Betsy entitled to make such a statement - based on the earth-shattering observation that "six equals three times two"?

NBER-NSF Time-Series Conference

The 2013 NBER-NSF Time Series Conference is being hosted by the Federal Reserve Board, in Washington D.C. next month. You can read about this event here.

Even a cursory look at the conference program will convince you that there are some really interesting looking papers being presented by some top people at this conference.

Check out the program, and you'll see what I mean. I'm going to be contacting several of the authors for access to their papers and talks. 

© 203, David E. Giles

In Praise of a Good Abstract

When you're writing up your research, it's a good idea to keep in mind that a lot of the potential readers of your exciting new paper are going to be busy people. I'm not talking about journal editors and referees - they're busy too, but they have an obligation to read your paper carefully. 

The rest of us have no such obligation, so you have to convince us that your research results are as interesting and important to us as they are to you.

I read a lot of papers dealing with econometrics and various areas of statistics. I also "pass over" even more papers that come my way via emails, web pages, and the like. 

Sometimes I'm following particular researchers/authors because I know from past experience that their work will be of interest to me. Otherwise, the title might catch my eye, and then I'll go as far as reading the abstract, and maybe the concluding section. Depending on the impression I've gained by that stage, I may or may not read the paper itself.

I think that, in this respect, I'm pretty typical of most of my colleagues. So, that's why the abstract of your paper is crucially important.

dataZoa

You may have noticed that in the past few of days some promotional links for dataZoa^™ have appeared in the lower part of the right side-bar of this blog page.

Usually, I don't go in for this sort of thing. However, I decided to make an exception in this case. Just so you know - I was not asked to do this, I'm getting nothing out of this, and I have no financial interest in dataZoa^™.

I simply wanted to share information about a really, really, nice resource. So, let me tell you just a little about it, and then you can go and explore dataZoa™ for yourselves.

The Stats Chat Blog

Recently, I've begun following the Stats Chat blog. Run by the Department of Statistics at the University of Auckland - the largest statistics department in New Zealand or Australia (and the birthplace of R) - this blog apparently started in April of this year.

It's aim is:

"to foster discussion of data around us, particularly in the media, and build an archive of resources for the general public, journalists and teachers".

Although the posts may appear to have a heavy N.Z. orientation, the topics covered are definitely of interest to a broader audience. I especially recommend this blog to students with an interest in statistics and/or econometrics.

You'll see interesting material, presented by members of a talented statistics group that has a long history of excellence.

Footnote:

I love the Department's (and blog's) by-line:

"Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write." – H.G. Wells.

© 2013, David E. Giles

Great Data Charts Using WebGL

I had an email today from Matt Hergott, who wrote:

"I notice you place an emphasis on charts and graphs. Many analyses could be helped by your suggestion that software offer charts of the data before running a regression. Along these lines, you might want to look at my new website: www.artemis-econometrics.com .

It contains four interactive three-dimensional scenes pertaining to econometrics and finance. The first graph is a simulation that makes it easy to spot outliers in a regression with two explanatory variables. The 3-D interactivity is important because people generally need different perspectives to see where the residuals are located.

I programmed these charts in JavaScript and WebGL. Now that Microsoft has decided to include WebGL in the upcoming Internet Explorer 11, it means that all major desktop browsers will support WebGL in the near future. This could open up a new frontier in the communication of quantitative concepts and results."

Matt's charts are really impressive. I must confess I really didn't know anything about WebGL (my loss) until he brought it to my attention.

It looks as if there are exciting times ahead!

© 2013, David E. Giles

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":