Musical Econometrics

There's a recent paper by McIntosh et al. (2013), titled "Listen to Your Data: Econometric Model Specification Through Sonification" that I really enjoyed. It's thought-provoking and innovative, and it takes things a lot further than what I mentioned in a previous post on data sonification.

Here's the abstract:

Allocation Models With Bounded Dependent Variables

My post yesterday, on Allocation Models, drew a comment to the effect that in such models the dependent variables take values that must to be non-negative fractions. Well, as I responded, that's true sometimes (e.g., in the case of market shares); but not in other cases- such as the Engel curve example that I mentioned in the post.

The anonymous comment was rather terse, but I'm presuming that the point that was intended is that if the y variables have to be positive fractions, we wouldn't want to use OLS. Ideally, that's so. Of course, we could use OLS and then check that all of the within-sample predicted values are between zero and one. Better still, we could use a more suitable estimator - one that takes the restriction on the data values into account.

The obvious solution is to assume that the errors, and hence the y values, follow a Beta distribution, and then estimate the equations by MLE. As I noted in my response to the comment, the "adding up" restictions that are needed on the parameters will be satisfied automatically, just as they are under OLS estimation.

Here's a demonstration of this.

Paper With Jacob Schwartz

It was nice to get the final "acceptance" yesterday for a paper co-authored with former grad. student, Jacob Schwartz.

The paper, titled "Bias-Reduced Maximum Likelihood Estimation of the Zero-Inflated Poisson Distribution", and with Jacob as lead author, will appear in Communications in Statistics - Theory & Methods. You can download a copy of the paper from here.

Jacob has been in the Ph.D. program at UBC for a while now. It seems quieter around the computing lab. without him!

© 2013, David E. Giles

Allocation Models

An "allocation model" is a special type of multi-equation model that has some interesting properties. This type of model arises quite frequently in applied econometrics, and it's worth knowing about it. In this post I'll explain what an allocation model is, and explore some of the estimation results that arise.

Ms DOS

They say that, with children, it doesn't get "easier", it just gets "different". Well, I'm not so sure. I have four grown-up "children" - they're are all successfully following their dreams, and I couldn't be happier!

So, I hope that Emma doesn't mind if I share this story from the mid 1990's, when her age was in single digits.

The Adjusted R-Squared, Again

In an earlier post about the adjusted coefficient of determination, R_A², I mentioned the following results that a lot of students don't seem to be aware of, in the context of a linear regression model estimated by OLS:

1. Adding a regressor will increase (decrease) R_A² depending on whether the absolute value of the t-statistic associated with that regressor is greater (less) than one in value. R_A² is unchanged if that absolute t-statistic is exactly equal to one. If you drop a regressor from the model, the converse of the above result applies.
2. Adding a group of regressors to the model will increase (decrease) R_A² depending on whether the F-statistic for testing that their coefficients are all zero is greater (less) than one in value. R_A² is unchanged if that  F-statistic is exactly equal to one. If you drop a group of regressors from the model, the converse of the above result applies.

The first of these results is (effectively) stated as Therorem 3.1 in Greene (2012), but the proof is left as an exercise.

In a comment on my previous  post, I was asked if I could supply simple proofs of these results.

Connections Between Univariate Distributions

I've been enjoying Francis X. Diebold's blog, No Hesitations. The other day he had a nice post on statistical graphics, and I found myself nodding (affirmatively) as I read through it. I won't repeat his points here, save to say:

• I, too, am a great fan of Edward Tufte. I have a couple of his books, and I used to use Minard's Napoleon chart in my introductory descriptive statistics courses.
• I have a copy of the chart of univariate statistical distribution relationships (Leemis et al., 2008) on my office wall. I was delighted to learn, from Francis's blog, that an interactive version of this chart is available.

The interactive version is definitely worth taking a look at.

© 2013, David E. Giles

Summer Reading

The schools are out, and here in Canada we celebrated Canada Day yesterday. That means it's now summer! And summer means summer reading.

So, here are some suggestions for you:

• Andreou, E., E. Ghysels, and A. Kourtellos, 2013. Should macroeconomic forecasters use daily financial data and how? Journal of Business and Economic Statistics, 31, 240-251.
• Downey, A. B., 2013. Think Bayes: Bayesian Statistics Made Simple. Green Tea Press, Needham MA.
• Espejo, M. R., M. D. Pineda, and S. Nadarajah, 2013. Optimal unbiased estimation of some population central moments. Metron, 71, 39-62.
• Giacomini, R., D. M. Politis, and H. White, 2013. A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators. Econometric Theory, 29, 567-589.
• Hayter, A. J., 2013. A new procedure for the Behrens-Fisher problem that guarantees confidence levels. Journal of Statistical Theory and Practice, 7, 515-536.
• Ouysse, R., 2013. Forecasting using a large number of predictors: Bayesian model averaging versus principal components regression. Australian School of Business Working Paper 2013 ECON 04, University of New South Wales.
• Pinkse, J., 2013. The ET interview: Herman Bierens. Econometric Theory, 29, 590-608.
• Stigler, S. M., 2007.  The epic story of maximum likelihood. Statistical Science, 22, 598-620.
• Yu, P., 2013. Inconsistency of 2SLS estimators in threshold regression with endogeneity. Economics Letters, in press.

© 2013, David E. Giles

N.Z. Association of Economists Conference

Although it's still the afternoon of Tuesday 2 July here on the We(s)t Coast, it's already the morning of Wednesday 3 July in New Zealand. That being the case, the 54th Annual Conference of the New Zealand Association of Economists is just getting underway in Wellington. Although I'm not attending, I do have a soft-spot for this conference, and I'll be participating next year.

The conference program includes a number of interesting looking empirical papers, and as usual there is a strong emphasis on economic policy analysis.

The other reason for my interest in this conference? The first conference paper I ever presented was at the 1972 NZAE Conference, held at Massey University in Palmerston North. I talked about "Consumption Expenditure in New Zealand". How time flies!

© 2013, David E. Giles

Congratulations, Graham Voss!

Congratulations to my departmental colleague, Graham Voss, whose promotion to full Professor takes effect today!

Graham describes his research interests as: "Applied macroeconomics with a focus on monetary and fiscal policies and exchange rates". He's a very accomplished empirical macroeconomist, with extensive experience at The Reserve Bank of Australia (their central bank) to complement his academic contributions.

Here's his webpage.

© 2013, David E. Giles