Monday, April 21, 2014

More On the Limitations of the Jarque-Bera Test

Testing the validity of the assumption, that the errors in a regression model are normally distributed, is a standard pastime in econometrics. We use this assumption when we construct standard confidence intervals  for, or test hypotheses about, the parameters of our models. In a post some time ago I pointed out that this assumption is actually is sufficient, but not necessary, for the validity of these inferences.

More recently, here and here, I discussed some aspects of the normality test that most econometricians use - the asymptotically valid test of Jarque and Bera (1987). Let's refer to this as the JB test. In the first of those posts I made brief mention of the finite-sample properties of the JB test, and I concluded:
"However, more recent evidence suggests that the power of the J-B test can be quite low in small samples, for a number of important alternative hypotheses - e.g., see Thadewald and Buning (2004). I'll address this aspect of the J-B test more fully in a later post."
The main results obtained by Thadewald and Buning are summed up in the abstract to their paper .............

Ray Fair's Model(s) in EViews

Here's a follow-up to my recent post about the Federal Reserve U.S. macroeconometric model being freely available in EViews format

Ray Fair's well-known model for the U.S. economy is also now available in a form that's ready to play with in EViews. See here. This is a great teaching tool, and a terrific resource for econometrics students.

In case you're looking for some special fun, Ray is looking for someone to convert his multi-country (MC) model into EViews format, so that it will also be freely available to all of us. The MC model covers 38 countries, and is described here.

HT to Gareth at IHS EViews for alerting me to these developments.




© 2014, David E. Giles

Friday, April 18, 2014

Welcome to Econometrics Students in China

One of my students mentioned to me yesterday that there was quite a bit of action on Weibo (the Chinese equivalent to Twitter) relating to posts on this blog - especially those posts relating to MCMC methods in econometrics. That's just great - thanks for your interest!

Looking at the stats. associated with the page-views for this blog, I see that in the last week China ranks number 3 (after the U.S. and the U.K.) as the most frequent country of origin. Over the past month China is number 4, being beaten only very slightly by Canada.

This certainly was't the case even 3 months ago.


© 2014, David E. Giles

Wednesday, April 16, 2014

An Exercise With the SURE Model

Here's an exercise that I sometimes set for students if we're studying the Seemingly Unrelated Regression equations (SURE) model. In fact, I used it as part of a question in the final examination that my grad. students sat last week.

Suppose that we have a 2-equation SURE model:

                        y1 = X1β1 + ε1

                        y2 = X2β2 + ε2  ,

where the sample is "balanced" (i.e,. we have n observations on all of the variables in both equations), and the errors satisfy the usual assumptions for a SURE model:

                     E[ε] = 0  ;  V(ε) = (Σ ⊗ In
where                ε' = [ε1' , ε2']' .

Exercise:  Prove that the SURE estimators of β1 and β2 are identical to the OLS estimators of β1 and β2 if the condition, X(X1'X1)-1 X1' = X(X2'X2)-1 X2' , is satisfied.

Viren Srivastava and I gave this as Exercise 2.14 in our 1987 book on the SURE model. However, we didn't give the solution there - so don't think you can cheat in that way!

You can see that the above condition is satisfied if X1 = X2, and the latter condition is one that is mentioned in most econometrics textbooks. However, it's much more stringent than is needed to get the result.

Also, the above condition is necessary, as well as sufficient, for the OLS and SURE estimators to coincide. However, that's another matter.

I'll post the "solution" to the exercise in a few days' time.


Reference

Srivastava, V. K. and D. E. A. Giles, 1987. Seemingly Unrelated Regression Equations Models:Estimation and Inference. Marcel Dekker, New York. 



© 2014, David E. Giles

Tuesday, April 15, 2014

Econometric Game, 2014

I've blogged about The Econometric Game previously - see here, here,  and here.

It's April, so the Game is on again - today and the next two days, to be specific. You can check out he details, as they become available, at this site.

Good luck to all of the participating teams!


Update, 17 April: And the winner is - The University of Copenhagen.

© 2014, David E. Giles

Sunday, April 13, 2014

Edmond Malinvaud on the Contributions of the Cowles Commission

"A father cannot expect more than to see his son take up his business and find new ways of making it flourish. Cowles econometricians of the forties are truly the fathers of present day econometricians and, like successful fathers, have good reason to be proud."
These are the closing remarks in an insightful historical perspective by Edmond Malinvaud, on the occasion of the fiftieth anniversary of the Cowles Commission. Malinvaud's piece, "Econometric Methodology at the Cowles Commission: Rise and Maturity", appeared in the Cowles Fiftieth Anniversary Volume

I urge all students of econometrics to read this enlightening account of the crucial role played by the affiliates of the Cowles Commission, first in Chicago, and subsequently (and still) at Yale University.

Malinvaud sums up this role succinctly as follows:
"The Cowles Commission contributed to the rise of econometric methodology in two determinate ways. On the one hand, it imposed "the probability approach": each application should begin with the definition of a precise stochastic model representing the phenomenon under study and the generation of the data; the method to be used for inference should then be rigorously determined within the framework of this model. On the other hand, it showed why most models to be built by economists should appear as systems of equations disturbed by additive random terms and often containing the values taken by the same variables in a few successive observations; it then fully determined methods to be recommended for estimation or testing within such models."
If you've been following my posts on "vintage years in econometrics", then you'll know that in the 1940's and 1950's, research at Cowles reigned supreme. Malinvaud, again:
"The major work for the building of simultaneous-equation econometrics at Cowles took place during the five and one-half years that roughly coincided with Jacob Marschak's term as director of research (January 1943 to June 1948). In the report for 1943, it appears that a good half of the research done during the year belonged to the simultaneous-equation econometrics field, although still with a definite orientation toward applied questions (demand functions, production functions, multiplier models). The presentation of this work already stresses the general methodological issues that were becoming the object of major concern. Not much later, the Cowles Commission called what turned out to be the most influential conference on statistical inference in economics ever held. It took place in Chicago from January 27 to February 1, 1945, and was attended by R.L. Anderson, T. Haavelmo, H. Hotelling, L. Hurwicz, L.R. Klein, T.C. Koopmans, R. Leipnik, H.B. Mann, J. Marschak, H. Rubin, G. Tintner, and A. Wald. The Commission research staff had prepared a number of papers dealing with various subjects, concerning in particular time-series analysis. The most novel contribution was certainly the one presented by Tjalling Koopmans and his research assistant Herman Rubin; it discussed both identification and maximum likelihood estimation in simultaneous-equation systems, proving the main theoretical results on both questions.
The report of the conference was prepared, with contributions made by other participants and with additions of subsequent work done at Cowles. These additions concerned mainly some theoretical developments; computational questions, which at this precomputer time might have been a real obstacle; and the "limited information" method of estimation, which was conceived in early 1946 by T.W. Anderson and H. Rubin and subsequently fully worked out by them. This report was to become Cowles Commission Monograph No. 10, Statistical Inference in Dynamic Economic Models, edited by T.C. Koopmans. We know that the manuscript was completed in early 1947, but publication was delayed until 1950 by typographical and other printing difficulties."
And of course, the over-identification test that was proposed in the Anderson-Rubin paper, has received significant, renewed, attention in recent research.

To sum up:
"When we look back and try to give a broad evaluation of the achievement of the simultaneous-equation work of the 1940s, we of course know that the theory was not complete by the end of this period. Alternative estimators had to be discovered, small-sample properties to be investigated, nonlinear simultaneous-equation models to be considered, efficient computational softwares to be built, even pedagogical presentations of the theory and of its algebra to be found. Nevertheless, after thirty more years of theoretical research in this field, the Cowles Commission construction essentially stands untouched; new wings and pinions have been added, good maps have been drawn, but the central building needs no repair. This was a perfectly sound and impressive piece of methodological work. No doubt or questioning can be expressed in this respect."


© 2014, David E. Giles

Law-Breaking Econometricians

I don't follow Lars P. Syll's blog, but the other day I was led there by a Twitter tweet. Lars begins his recent post, "Forecasting Alchemy", with the following statement:
'In New York State, Section 899 of the Code of Criminal Procedure provides that persons “Pretending to Forecast the Future” shall be considered disorderly under subdivision 3, Section 901 of the Code and liable to a fine of $250 and/or six months in prison."
Although the law does not apply to “ecclesiastical bodies acting in good faith and without fees,” I’m not sure where that leaves econometricians and other forecasters …'
I'm not sure either, but I'm not going to lose sleep over this unless I happen to re-locate to NY State.

Other economists have also drawn attention to this rather alarming piece of legislation, including Joan Robinson on page 8 of her 1981 book, What are the Questions?: And Other Essays: Further Contributions to Modern Economics.

Walter A. Friedman's recent book, Fortune Tellers: The Story of America's Economic Forecasters provides some insights into the origins of economic forecasting, and perhaps into that of Section 899. (See here for an excerpt.)



© 2014, David E. Giles

Open Science Through R

There's so much being written about R these days, and justifiably so. If you use R for your econometrics, you should also keep in mind that its applicability is far wider than statistical analysis. 

A big HT to the folks at Quandl for leading me to a nice overview of the way in which R is enabling some big changes in the way in which scientific research is being conducted more generally. The article in question is by Tina Amirtha, "How the Rise of the "R" Language is Bringing Open Source to Science", which you'll find here.

If you think that R is just about statistics, and you can't see the point of investing some time (not money) in getting on board, then read Tina's piece. 

You'll change your mind if you consider yourself a survivor.



© 2014, David E. Giles

Thursday, April 10, 2014

Proof of a Result About the "Adjusted" Coefficient of Determination

In a post last year I discussed the conditions under which the "adjusted" coefficient of determination (RA2) will increase or decrease, when regressors are deleted from (added to) a regression model. Without going over the full discussion again, here is one of the key results:

Adding a group of regressors to the model will increase (decrease) RA2 depending on whether the F-statistic for testing that their coefficients are all zero is greater (less) than one in value. RA2 is unchanged if that  F-statistic is exactly equal to one.

A few days ago, "Zeba" reminded me that I had promised to post a simple proof of this result, but I still hadn't done so. Shame on me! A proof is given below. As a bonus, I've given the proof for a more general result - we don't have to be imposing "zero" restrictions on some of the coefficients - any exact linear restrictions will suffice.

Let's take a look at the proof.

Friday, April 4, 2014

There's an App for That

I was looking for econometrics-related "apps" for my Android tablet. Very little of interest came up for "Econometrics", but there certainly are some nice data-related apps.

Here are a few examples:



© 2014, David E. Giles