Showing posts with label 2SLS. Show all posts
Showing posts with label 2SLS. Show all posts

Friday, July 11, 2014

Finite-Sample Properties of the 2SLS Estimator

During a recent conversation with Bob Reed (U. Canterbury) I recalled an interesting experience that I had at the American Statistical Association Meeting in Houston, in 1980. I was sitting in a session listening to an author presenting a paper about the bias and MSE of certain simultaneous equations estimators. The results were based on a Monte Carlo experiment. However, something just didn't seem right.

I looked at the guy sitting next to me - I didn't know him, but he was also looking puzzled. Then, at the same time, we both said to each other, "But the first two moments of that estimator don't exist!" The next thing out of our mouths was, "Who's going to tell him?"

The guy next to me turned out to be Tom Fomby, and I believe he was the one who politely explained to the speaker that his results were nonsensical.

If (the sampling distribution of) an estimator doesn't have a well-defined mean then it's nonsensical to talk that estimator's bias. Equally, if it doesn't have a well-defined variance, then it makes no sense to talk about its MSE. In other words, the Monte Carlo simulation results were trying to measure something that didn't exist! 

So, what was going on here?

Monday, April 21, 2014

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

Sunday, July 14, 2013

Vintage Years in Econometrics - The 1950's

Following on from my earlier posts about vintage years for econometrics in the 1930's and 1940's, here's my run-down on the 1950's.

As before, let me note that "in econometrics, what constitutes quality and importance is partly a matter of taste - just like wine! So, not all of you will agree with the choices I've made in the following compilation."

Tuesday, July 2, 2013

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

Tuesday, June 11, 2013

What Have You Been Reading?

Here are some of the papers that I was reading last week:
  • Arel-Bundock, V., 2013. A solution to the weak instrument bias in 2SLS estimation: Indirect inference with stochastic approximation, Economics Letters, in press.
  • Behar, R., P. Grima, and L. Marco-Almagro, 2013. Twenty-five analogies for explaining statistical concepts. American Statistician, 67(1), 44-48.
  • Chang, C-L., P. H. Frances, and M. McAleer, 2013, Are forecast updates progressive? MPRA Paper No. 46387.
  • Chortareas, G., and G. Kapetanios, 2013. How puzzling is the PPP puzzle? An alternative half-life measure of convergence to PPP. Journal of Applied Econometrics, 28, 435-457.
  • Davidson, R. and J. B. MacKinnon, 1998. Graphical methods for investigating the size and power of hypothesis tests. Manchester School, 66, 1-26.
  • Hood, W. C. and T. C. Koopmans, 1953. Studies in Econometric Method. Cowles Commission Monograph for Research in Economics, Monograph No. 14. Wiley, New York.
  • Kourouklis, S., 2012. A new estimator of the variance based on minimizing mean squared error. American Statistician, 66(4), 234-236.
  • Lanne, M. and P. Saikkonen, 2013. Noncausal vector autoregression. Econometric Theory, 29, 447-482.

© 2013, David E. Giles

Sunday, May 12, 2013

What's Your Favourite Estimator?

It's interesting to dwell on the popularity of different estimators that econometricians use. Some estimators are "in vogue" for a period, and then give way to others as new developments come along. Different topics have captured the attention of theoreticians and practitioners alike at different times in history.

Here's a Google Ngram showing the extent to which some familiar estimators for simultaneous equations models have been mentioned in books since 1960:

Not too surprisingly, good old OLS just goes on and on:

I was going to include the GMM estimator in these plots, but this acronym has meanings other than the obvious one that comes to mind. So, the results would have been misleading. To be safe, let's use the full phrase Generalized Method of Moments and allow for case sensitivity:

Interestingly, the phrase appeared in some books before the publication of Hansen's classic 1982 paper.

© 2013, David E. Giles

Monday, March 4, 2013

Measuring the Quality of an Estimator

In which, with almost no symbols, I encourage students and practitioners to question what they've been taught............

When it comes to introducing our students to the notion of the "quality" of an estimator, most of us begin by observing that estimators are functions of the random sample data, and hence they are "statistics" in the literal sense. As such, estimators have a probability distribution. We give this distribution a special name - the "sampling distribution" of the estimator in question.

It's understandable that students sometimes find the concept of the sampling distribution a little tricky when they first encounter it. After all, it's based on a "thought game" of sorts. We have to consider the idea of repeatedly drawing samples of a fixed size, for ever, constructing the statistic in question, and then keeping track of all of the possible values that the statistic can take, together with the relative frequency of occurrence for each value. A Monte Carlo experiment is the obvious way to introduce students to this concept.

Sunday, October 7, 2012

Dancing With the Econometricians

Let's talk about the two-step. Not the tango or the polka. The two-step!

More specifically let's talk about a particular two-step estimator that we use all of the time in econometrics. I want to clear up some misconceptions that I seem to encounter all too frequently when I read empirical "applied" papers.

Why is it that some people insist on using the term "Two Stage Least Squares" inappropriately? 

Let me explain what I mean.