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

The Bootstrap - A Non-Technical Introduction

Computer-intensive methods have become essential to much of statistical analysis, and that includes econometrics. Think of Monte Carlo simulations, MCMC for Bayesian methods, maximum simulated likelihood, empirical likelihood methods, the jackknife, and (of course) the bootstrap.

Although we usually date the bootstrap from Bradley Efron's 1979 paper, as a resampling method it has its roots in earlier, related, contributions including those of Quenouille (1949, 1956).

The main purpose of this post is to draw readers' attention to the piece by Diaconis and Efron (1983) that appeared in Scientific American. It's written for a "general audience", which is nice, and it also provides an interesting snapshot of what was cutting-edge computing 30 years ago. The discussion paper version of the article (including typos) is available here.

As a final bonus, the examples include one from econometrics!


References

Diaconis and B. Efron, 1983. Computer intensive methods in statistics. Scientific American, 248, 116-132.

Efron, B., 1979. Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.

Quenouille, M. H.,1949. Approximate tests of correlation in time series. Journal of the Royal

Statistical Society, Series B, 11, 18-44.

Quenouille, M. H.,1956. Notes on bias in estimation. Biometrika, 61, 353-360.

© 2013, David E. Giles

Free Download of My Recent Paper

If you're interested, you can download a copy of one of my recent papers, with Helen Feng and Ryan Godwin, for free from the publisher's website.

The paper in question is titled, "On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution", Communications in Statistics - Theory and Methods, 2013, 42, 1934-1950.

Only the first 50 downloads are free, so if you're interested you'd better get cracking!

© 2013, David E. Giles

Can You Actually TEST for Multicollinearity?

When you're undertaking a piece of applied econometrics, something that's always on your mind is the need to test the specification of your model, and to test the validity of the various underlying assumptions that you're making. At least - I hope it's always on your mind!

This is an important aspect of any modelling exercise, whether you're working with a linear regression model, or with some nonlinear model such Logit, Probit, Poisson regression, etc. Most people are pretty good when it comes to such testing in the context of the linear regression model. They seem to be more lax once they move away from that framework. That makes me grumpy, but that's not what this particular post is about.

It's actually about a rather silly question that you sometimes encounter, namely: "Have you tested to see if multicollinearity is a problem for your results?"

I'll explain why this isn't really a sensible question, and why the answer to the question in the title for this post is a resounding "No!"