Monte Carlo Simulation Basics, I: Historical Notes

Monte Carlo (MC) simulation provides us with a very powerful tool for solving all sorts of problems. In classical econometrics, we can use it to explore the properties of the estimators and tests that we use. More specifically, MC methods enable us to mimic (computationally) the sampling distributions of estimators and test statistics in situations that are of interest to us. In Bayesian econometrics we use this tool to actually construct the estimators themselves. I'll put the latter to one side in what follows.

The BMST Package for Gretl

As a follow-up to this recent post, I heard again from Artur Tarassow.

You'll see from his email message below that he's extended his earlier work and has prepared a new package for Gretl called "Binary Models Specification Tests".

It's really good to see tests of this type being made available for users of different software - especially free software such as Gretl.

Artur writes:

Snakes in a Room

Teachers frequently use analogies when explaining new concepts. In fact, most people do. A good analogy can be quite eye-opening.

The other day my wife was in the room while I was on the 'phone explaining to someone why we often like to apply BOTH the ADF test and the KPSS test when we're trying to ascertain whether a partcular time-series is stationary or non-stationary. (More specifically, whether it is I(0) or I(1).) The conversation was, not surprisingly, relatively technical in nature.

After the call was over, it occurred to me that my wife (who is an artist, and not an econometrician) might ask me what the heck all that gobbly-gook was all about. As it happened, she didn't - she had more important things on her mind, no doubt. But it forced me to think about a useful analogy that one might use in this particular instance.

I'm not suggesting that what I came up with is the best possible analogy, but for what it's worth I'll share it with you.

November Reading

You'll see that this month's reading list relates, in part, to my two recent posts about Ted Anderson and David Cox.

• Acharya, A., M. Blackwell, & M. Sen, 2015. Explaining causal findings without bias: Detecting and assessing direct effects. RWP15-194, Harvard Kennedy School.
• Anderson, T.W., 2005. Origins of the limited information maximum likelihood and two-stage least squares estimators. Journal of Econometrics, 127, 1-16.
• Anderson, T.W. & H. Rubin, 1949. Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics, 20, 46-63.
• Cox, D.R., 1972. Regression models and life-tables (with discussion). Journal of the Royal Statistical Society B, 34, 187–220.
• Malsiner-Walli, G. & H. Wagner, 2011. Comparing spike and slab priors for Bayesian variable selection. Austrian Journal of Statistics, 40, 241-264.
• Psaradakis, Z. & M. Vavra, 2016. Portmanteau tests for linearity of stationary time series. Working Paper 1/2016, National Bank of Slovakia.

© 2016, David E. Giles

T. W. Anderson: 1918-2016

Unfortunately, this post deals with the recent loss of one of the great statisticians of our time - Theodore (Ted) W. Anderson.

Ted passed away on 17 September of this year, at the age of 98.

I'm hardly qualified to discuss the numerous, path-breaking, contributions that Ted made as a statistician. You can read about those in De Groot (1986), for example.

However, it would be remiss of me not to devote some space to reminding readers of this blog about the seminal contributions that Ted Anderson made to the development of econometrics as a discipline. In one of the "ET Interviews", Peter Phillips talks with Ted about his career, his research, and his role in the history of econometrics.  I commend that interview to you for a much more complete discussion than I can provide here.

(See this post for information about other ET Interviews).

Ted's path-breaking work on the estimation of simultaneous equations models, under the auspices of the Cowles Commission, was enough in itself to put him in the Econometrics Hall of Fame. He gave us the LIML estimator, and the Anderson and Rubin (1949, 1950) papers are classics of the highest order. It's been interesting to see those authors' test for over-identification being "resurrected" recently by a new generation of econometricians. 

There are all sorts of other "snippets" that one can point to as instances where Ted Anderson left his mark on the history and development of econometrics.

For instance, have you ever wondered why we have so many different tests for serial independence of regrsssion errors? Why don't we just use the uniformly most powerful (UMP) test and be done with it? Well, the reason is that no such test (against the alternative of a first-oder autoregresive pricess) exists.

That was established by Anderson (1948), and it led directly to the efforts of Durbin and Watson to develop an "approximately UMP test" for this problem.

As another example, consider the "General-to-Specific" testing methodology that we associate with David Hendry, Grayham Mizon, and other members of the (former?) LSE school of thought in econometrics. Why should we "test down", and not "test up" when developing our models? In other words, why should we start with the most  general form of the model, and then successively test and impose restrictions on the model, rather than starting with a simple model and making it increasingly complex? The short answer is that if we take the former approach, and "nest" the successive null and alternative hypotheses in the appropriate manner, then we can appeal to a theorem of Basu to ensure that the successive test statistics are independent. In turn, this means that we can control the overall significance level for the set of tests to what we want it to be. In contrast, this isn't possible if we use a "Simple-to-General" testing strategy.

All of this spelled out in Anderson (1962) in the context of polynomial regression, and is discussed further in Ted's classic time-series book (Anderson, 1971). The LSE school referred to this in promoting the "General-to-Specific" methodology.

Ted Anderson published many path-breaking papers in statistics and econometrics and he wrote several books - arguably, the two most important are Anderson (1958, 1971). He was a towering figure in the history of econometrics, and with his passing we have lost one of our founding fathers.

References

Anderson, T.W., 1948. On the theory of testing serial correlation. Skandinavisk Aktuarietidskrift, 31, 88-116.

Anderson, T.W., 1958. An Introduction to Multivariate Statistical Analysis. WIley, New York (2nd. ed. 1984).

Anderson, T.W., 1962. The choice of the degree of a polynomial regression as a multiple decision problem. Annals of Mathematical Statistics, 33, 255-265.

Anderson, T.W., 1971. The Statistical Analysis of Time Series. Wiley, New York.

Anderson, T.W. & H. Rubin, 1949. Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics, 20, 46-63.

Anderson, T.W. & H. Rubin, 1950. The asymptotic properties of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics, 21,570-582.

De Groot, M.H., 1986. A Conversation with T.W. Anderson: An interview with Morris De Groot. Statistical Science, 1, 97–105.

© 2016, David E. Giles

I Was Just Kidding......!

Back in 2011 I wrote a post that I titled, "Dummies for Dummies". It began with the suggestion that I'd written a book of that name, and it included this mock-up of the "cover":

(Thanks to former grad. student, Jacob Schwartz, for helping with the pic.)

Although I did say, "O.K., I'm (uncharacteristically) exaggerating just a tad", apparently a few people took me too seriously/literally. I've had a couple of requests for the book, and even one of my colleagues asked me when it would be appearing.

Sadly, no book was ever intended - somehow, I just don't think there's the market for it!

© 2016, David E. Giles

Specification Tests for Logit Models Using Gretl

In various earlier posts I've commented on the need for conducting specification tests when working with Logit and Probit models. (For instance, see here, here, and here.) 

One of the seminal references on this topic is Davidson and MacKinnon (1984). On my primary website, you can find a comprehensive list of other related references, together with EViews files that will enable you to conduct various specification tests with LDV  models.

The link for that material is here.

Today I had an email from Artur Tarassow at the University of Hamburg. He wrote:

I know that you're already aware of the open-source econometric software called "Gretl". 

I would like to let you know that I updated my package "LOGIT_HETERO.gfn". This package runs both the tests of homoskedasticity and correct functional form based on your nice program "Logit_hetero.prg" written for EViews.

If you want to have a look at it, simply run:

    set echo off

    set messages off

    install LOGIT_HETERO.gfn

    include LOGIT_HETERO.gfn

    open http://web.uvic.ca/~dgiles/downloads/binary_choice/Logistic_Burr.wf1

    logit Y 0 X1 X2

    matrix M = LOGIT_HETERO(Y,$xlist,$coeff,1)

    print M

Thanks for this, Artur - I'm sure it will be very helpful to many readers of this blog.

Footnote: See Artur's comment below, and the more recent post here. In particular, note Artur's comment: As a note to your blog readers: The two Logit model related packages “logit_burr.gfn” and “LOGIT_HETERO.gfn” are not available any more, as BMST includes both of them.

Reference

Davidson, R. & J. G. MacKinnon, 1984. Convenient specification tests for logit and probit models. Journal of Econometrics, 25, 241 262.

© 2016, David E. Giles

International Prize in Statistics

A few days ago, the inaugural winner of the biennial International Prize in Statistics was announced.

The first recipient of the new award is Sir David Cox, whose work is, of course, well known to econometricians.

The award was made to Sir David for his "Survival Analysis Model Applied in Medicine, Science, and Engineering".

Some Suggested Reading for October

For your enjoyment:

• Diebold, F. X. & M. Shin, 2016. Assessing point forecast accuracy by stochastic error distance. NBER Working Paper No.2516.
• Franses, P.H., 2016. Yet another look at MIDAS regression. Econometric Institute Report 2016-32.
• Hillier, G. & F. Martellosio, 2016. Exact properties of the maximum likelihood estimator in spatial autoregressive models. Discussion Paper DP 07/16, Department of Economics, University of Surrey.
• Li, L., M.J. Holmes, & B.S. Lee, 2016. The asymmetric relationship between executive earnings management and compensation: A panel threshold regression approach. Applied Economics, 48, 5525-5545. 
• Lütkepohl, H., A. Staszewska-Bystrova, & P. Winker, 2016. Calculating joint confidence bands for impulse response functions using highest density regions. MAGKS Joint Discussion Paper 16-2016.
• Segnon, M., R. Gupta, S. Bekiros, & M.E. Wohar, 2016. Forecasting U.S. GNP growth: The role of uncertainty. Working Paper 2016-67, Department of Economics, University of Pretoria.

© 2016, David E. Giles

Spreadsheet Errors

Five years ago I wrote a post titled, "Beware of Econometricians Bearing Spreadsheets". 

The take-away message from that post was simple: there's considerable, well-documented, evidence that spreadsheets are very, very, dangerous when it comes to statistical calculations. That is, if you care about getting the right answers!

Read that post, and the associated references, and you'll see what I mean.

(You might also ask yourself, why would I pay big bucks for commercial software that is of questionable quality when I can use high-quality statistical software such as R, for free?)

This week, a piece in The Economist looks at the shocking record of publications in genomics that fall prey to spreadsheet errors. It's a sorry tale, to be sure. I strongly recommend that you take a look.

Yes, any software can be mis-used. Anyone can make a mistake. We all know that. However, it's not a good situation when a careful and well-informed researcher ends up making blunders just because the software they trust simply isn't up to snuff!  

© 2016, David E. Giles