Forecasting From an Error Correction Model

Recently, a reader asked about generating forecasts from an estimated Error Correction Model (ECM). Really, the issues that arise are no different from those associated with any dynamic regression model. I talked about the latter in a previous post in 2013.

Anyway, let's take a look at the specifics.........

A Quick Illustration of Pre-Testing Bias

The statistical and econometric literature on the properties of "preliminary-test" (or "pre-test") estimation strategies is large and well established. These strategies arise when we proceed in a sequential manner when drawing inferences about parameters. 

A simple example would be where we fit a regression model; test if a regressor is significant or not; and then either retain the model, or else remove the (insignificant) regressor and re-estimate the (simplified) model.

The theoretical literature associated with pre-testing is pretty complex. However, some of the basic messages arising from that literature can be illustrated quite simply. Let's look at the effect of "pre-testing" on the bias of the OLS regression estimator.

Graduate Econometrics Exam

Occasionally readers ask about the exams that I set in my graduate econometrics courses.

The elective graduate econometrics course that I taught this past semester was one titled "Themes in Econometrics". The topics that are covered vary from year to year. However, as the title suggests, the course focuses on broad themes that arise in econometrics. Examples might include maximum likelihood estimation and the associated testing strategies;instrumental variables/GMM estimation; simulation methods; nonparametric inference; and Bayesian inference.

This year most of the course was devoted to maximum likelihood, and Bayesian methods in econometrics.

The mid-term test covered the first of these two thematic topics, while the final exam was devoted largely to Bayesian inference.

You can find the mid-term test here. The final exam question paper is here; and the associated R code is here.

© 2016, David E. Giles

Econometric Computing in the Good Ol' Days

I received an email from Michael Belongia, who said:

"I wrote earlier in response to your post about Almon lags but forgot to include an anecdote that may be of interest to your follow-up.

In the late 1960s, the "St. Louis Equation"  became a standard framework for evaluating the relative effects of monetary and fiscal policy. The equation was estimated by the use of Almon lags (see, e.g., footnotes 12 and 18 in the article).  To estimate the equation, however, the St. Louis Fed had to use the computing power of nearby McDonnell-Douglas!!!  As Keith Carlson, who was in the Bank's Research Dept at the time, confirmed for me:   

'We did send our stuff out to McDonnell-Douglas.  Gave the instructions to the page who took it to the Cotton Belt building at 4th and Pine and the output would be picked up a couple days later. We did this until about 67 or 68 when we shifted to in-house.  In fact we hired the programmer from M-D.'

Difficulties like this certainly made economists of the era think more carefully about their models before taking them to the data."

I concur wholeheartedly with Michael's last comment. My own computing experience began in the late 1960's - I've posted about this in the past in The Monkey Run.

And I haven't forgotten the follow-up post on Almon distributed lag models that I promised!

© 2016, David E. Giles

May Reading List

Here's my reading list for May:

• Hayakawa, K., 2016. Unit root tests for short panels with serially correlated errors. Communications in Statistics - Theory and Methods, in press.
• Hendry, D. F. and G. E. Mizon, 2016. Improving the teaching of econometrics. Discussion Paper 785, Department of Economics, University of Oxford.
• Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky, 1999. Bayesian model averaging: A tutorial (with comments and rejoinder). Statistical Science, 14, 382-417. 
• Liu, J., D. J. Nordman, and W. Q. Meeker, 2016. The number of MCMC draws needed to compute Bayeian credible bounds. American Statistician, in press.
• Lu, X., L. Su, and H. White, 2016. Granger causality and structural causality in cross-section and panel data. Working Paper No, 04-2016, School of Economics, Singapore Management University.
• Nguimkeu, P., 2016.  An improved selection test between autoregressive and moving average disturbances in regression models. Journal of Time Series Econometrics, 8, 41-54.

© 2016, David E. Giles

My Latest Paper About Dummy Variables

Over the years I've posted a number of times about various aspects of using dummy variables in regression models. You can use the "Search" window in the right sidebar of this page if want to take a look at those posts.

One of my earlier working papers on this topic has now been accepted for publication.

The paper is titled, "On the Inconsistency of Instrumental Variables Estimators for the Coefficients of Certain Dummy Variables". Here's the abstract:

"In this paper we consider the asymptotic properties of the Instrumental Variables (IV) estimator of the parameters in a linear regression model with some random regressors, and other regressors that are dummy variables. The latter have the special property that the number of non-zero values is fixed, and does not increase with the sample size. We prove that the IV estimator of the coefficient vector for the dummy variables is inconsistent, while that for the other regressors is weakly consistent under standard assumptions. However, the usual estimator for the asymptotic covariance matrix of the I.V. estimator for all of the coefficients retains its usual consistency. The t-test statistics for the dummy variable coefficients are still asymptotically standard normal, despite the inconsistency of the associated IV coefficient estimator. These results extend the earlier results of Hendry and Santos (2005), which relate to a fixed-regressor model, in which the dummy variables are non-zero for just a single observation, and OLS estimation is used".

You can download the final working paper version of the paper from here.

The paper will be appearing in an upcoming issue of Journal of Quantitative Economics.

© 2016, David E. Giles