July Reading

Now that the (Northern) summer is here, you should have plenty of time for reading. Here are some recommendations:

• Ahelegbey, D. F., 2015. The econometrics of networks: A review. Working Paper 13/WP/2015, Department of Economics, University of Venice.
• Camba-Mendez, G., G. Kapetanios, F. Papailias, and M. R. Weale, 2015. An automatic leading indicator, variable reduction and variable selection methods using small and large datasets: Forecasting the industrial production growth for Euro area economies. Working Paper No. 1773, European Central Bank.
• Cho, J. S., T-H. Kim, and Y. Shin, 2015. Quantile cointegration in the autoregressive distributed-lag modeling framework. Journal of Econometrics, 188, 281-300.
• De Luca, G., J. R. Magnus, and F. Peracchi, 2015. On the ambiguous consequences of omitting variables. EIEF Working Paper 05/15.
• Gozgor, G., 2015. Causal relation between economic growth and domestic credit in the economic globalization: Evidence from the Hatemi-J's test. Journal of International Trade and Economic Development,  24, 395-408.
• Panhans, M. T. and J. D. Singleton, 2015. The empirical economist's toolkit: From models to methods. Working Paper 2015-03, Center for the History of Political Economy.
• Sanderson. E and F. Windmeijer, 2015. A weak instrument F-test in linear IV models with multiple endogenous variables. Discussion Paper 15/644, Department of Economics, University of Bristol.

© 2015, David E. Giles

The Econometrics of Temporal Aggregation - VI - Tests of Linear Restrictions

This post is one of several related posts. The previous ones can be found here, here, here, here and here. These posts are based on Giles (2014).

Many of the statistical tests that we perform routinely in econometrics can be affected by the level of aggregation of the data. Here, Let's focus on time-series data, and with temporal aggregation. I'm going to show you some preliminary results from work that I have in progress with Ryan Godwin. These results relate to one particular test, but work covers a variety of testing problems.

I'm not supplying the EViews program code that was used to obtain the results below - at least, not for the moment. That's because the results that I'm reporting are based on work in progress. Sorry!

As in the earlier posts, let's suppose that the aggregation is over "m" high-frequency periods. A lower case symbol will represent a high-frequency observation on a variable of interest; and an upper-case symbol will denote the aggregated series.

So,

               Y_t = y_t + y_{t - 1} + ......+ y_{t - m + 1} .

If we're aggregating monthly (flow) data to quarterly data, then m = 3. In the case of aggregation from quarterly to annual data, m = 4, etc.

Now, let's investigate how such aggregation affects the performance of standard tests of linear restrictions on the coefficients of an OLS regression model. The simplest example would be a t-test of the hypothesis that one of the coefficients is zero. Another example would be the F-test of the hypothesis that all of the "slope" coefficients in such a regression model are zero.

Consider the following simple Monte Carlo experiment, based on 20,000 replications.

"Readers' Forum" Page

I've added a new page to this blog - it's titled "Readers' Forum". You'll see the tab for it in the bar just above the top post on the page you're reading now.

Some explanation is in order.

What?

The Readers' Forum is intended to be a "clearing house" for questions and requests relating to econometrics'

As I say in the preamble to the new page,

"Please feel free to use the "Comment" facility below to provide questions and answers relating to Econometrics. I won't be able to answer all questions myself, but other readers may be able to help. The Forum will be "lightly moderated" to avoid spam and inappropriate content."

Please note the italicized passage above.

Why?

Every day, readers post (or attempt to post) lots of "comments" on the various posts on this blog. In many cases, these are not comments at all - they're questions, requests for assistance, and the like.

All comments are moderated - I get to give them the "O.K." before they actually appear. That's just fine for genuine comments. Unless they're spam or contain inappropriate content, I invariably "approve" them right away.

However, in the case of questions and requests I prefer to delay approval and post a response simultaneously. Regrettably, this has meant that, increasingly, there is often a delay in getting this out there. 

Sometimes, the requests are, quite frankly, unreasonable.I won't go into the details here, but let's just say that there's a difference between a blog and a free consulting service.

I also try to be very careful when it's clear that the request comes form a student. I certainly don't want to get into a situation where I'm "getting between" that student and their instructor/supervisor.

In short, I like to try and be helpful, but I can't keep up with the demand. I do have a job!

Hopefully, the new forum will free up some time for me to focus on substantive posts, while still providing an opportunity for discussion.

© 2015, David E. Giles

Econometrics Videos

The Royal Economics Society (publisher of The Econometrics Journal) has recently released a video of invited addresses by Alfred Galichon and Jeremy Lise, in the special session on “Econometrics of Matching” at the 2015 RES Conference.

This video joins similar ones from previous RES conferences, these being:

• “Large Dimensional Models”, 
• ”Heterogeneity”,  
• “Econometrics of Forecasting”, 
•  “Nonparametric Identification” 

This link will take you to all of these videos.

Happy viewing!

© 2015, David E. Giles

Specification Testing in the Ordered Probit Model

Readers of this blog will know I'm a proponent of more specification testing in the context of Logit, Probit, and related models. For, instance, see this recent post, and the links within it.

I received an email from Paul Johnson, Chair of the Department of Economics at Vassar College, today. He wrote:

"I thought that, given your interest in specification tests in probit etc. models, you might find the attached paper of mine (written some years ago) to be useful as it expounds the straightforward generalization of the Bera, et al. (1984) test to the ordered probit case."

Paul's paper is, indeed, very interesting and I hadn't seen it before. It's titled, "A Test of the Normality Assumption in the Ordered Probit Model", and it appeared in the statistics journal, Metron (1996, LIV, 213-221).

Here's the abstract:

"This paper presents an easily implemented test of the assumption of a normally distributed error term for the ordered probit model, As this assumption is the central maintained hypothesis in all estimation and testing based on this model, the test ought to serve as a key specification test in applied research. A small Monte Carlo experiment suggests that the test has good size and power properties."

A year later, a closely related paper by P. Glewwe appeared in Econometric Reviews. That author doesn't mention Paul's paper, but these things happen. Glewwe's paper does take things a little further than Paul does, by allowing for censoring of the data.

© 2015, David E. Giles

Worrying About my Cholesterol Level

The headline, "Don't Get Wrong Idea About Cholesterol", caught my attention in the 3 May, 2015 Times-Colonist newspaper here in Victoria, B.C.. In fact the article came from a syndicated column, published about a week earlier. No matter - it's always a good time for me to worry about my cholesterol!

The piece was written by a certain Dr. Gifford-Jones (AKA Dr. Ken Walker).

Here's part of what he had to say:

Statistical Calculations & Numerical Accuracy

This post is for those readers who're getting involved with economic statistics for the first time. Basically, it serves as a warning that sometimes the formulae that you learn about have to be treated with care when it comes to the actual numerical implementation.

Sometimes (often) there's more than one way to express the formula for some statistic. While thee formulae may be mathematically identical, they can yield different numerical results when you go to apply them. Yes, this sounds counter-intuitive, but it's true. And it's all to do with the numerical precision that your calculator (computer) is capable of.

The example I'll give is a really simple one. However, the lesson carries over to more interesting situations. For instance, the inversion of matrices that we encounter when applying the OLS estimator is a case in point. When you fit a regression model using several different statistics/econometrics computer packages, you sometimes get slightly different results. This is because the packages can use different numerical methods to implement the algebraic results that you're familiar with.

For me, the difference between a "good" package and a "not so good" package isn't so much the range of fancy techniques that each offers at the press of a few keys. It's more to do with what's going on "under the hood". Do the people writing the code know how make that code (a) numerically accurate; and (b) numerically robust to different data scenarios?

Logit, Probit, & Heteroskedasticity

I've blogged previously about specification testing in the context of Logit and Probit models. For instance, see here and here. 

Testing for homoskedasticity in these models is especially important, for reasons that are outlined in those earlier posts. I won't repeat all of the details here, but I'll just note that heteroskedasticity renders the MLE of the parameters inconsistent. (This stands in contrast to the situation in, say, the linear regression model where the MLE of the parameters is inefficient, but still consistent in this case.)

If you're an EViews user, you can find my code for implementing a range of specification tests for Logit and Probit models here. These include the LM test for homoskedasticity that was proposed by Davidson and MacKinnon (1984).

More than once, I've been asked the following question:

"When estimating a Logit or Probit model, we set the scale parameter (variance) of the error term to the value one, because it's not actually identifiable. So, in what sense can we have heteroskedasticity in such models?"

This is a good question, and I thought that a short post would be justified. Let's take a look:

June Reading List

• Andrews, I. and T. B. Armstrong, 2015. Unbiased instrumental variables estimation under known first-stage sign. Cowles Foundation Discussion Paper No. 1984R, Yale University,
• Bajari, P., D. Nekipelov, S. P. Ryan, and M. Yang. 2015. Demand estimation with machine learning and model combination. NBER Working Paper 20955.
• Chambers, M. J., 2015. A jackknife correction to a test for cointegration rank. Econometrics, 3, 355-375.
• Mazeu, J. H. G., E. Ruiz and H. Veiga, 2015. Model uncertainty and the forecast accuracy of ARMA models: A survey. UC3M Working Paper 15-08, Statistics and Econometrics, Universidad Carlos III de Madrid. 
• Paldam, M., 2015. Meta-analysis in a nutshell: Techniques and general findings. Economics, 9, 2015-11.
• Triacca, U., 2015. A pitfall in using the characterization of Granger non-causality in vector autoregressive models. Econometrics, 3, 233-239.

© 2015, David E. Giles