Reading for the Holidays

Here are some suggestions for your Holiday reading:

• Athey, S. and G. Imbens, 2016. The state of econometrics - Causality and policy evaluation. Mimeo., Graduate School of Business, Stanford University.
• Cook, J. D., 2010. Testing a random number generator. Chapter 10, in T. Rily and A. Goucher (eds.), Beautiful Testing, O' Reilly Media, Sebastol, CA. 
• Ivanov, V. and L. Kilian, 2005. A practitioner's guide to lag order selection for VAR impulse response analysis. Studies in Nonlinear Dynamics and Econometrics, 9, article 2.
• Polanin, J. A., E. A. Hennessy, and E. E. Tanner-Smith, 2016. A review of meta-analysis packages in R. Journal of Educational and Behavioural Statistics, 42, 206-242.
• Young, A., 2017. Consistency without inference: Instrumental variables in practical application. Mimeo.,  London School of Economics.
• Zhang, L., 2017, Partial unit root and surplus-lag Granger causality testing: A Monte Carlo simulation study. Communications in Statistics - Theory and Methods, 46, 12317-12323.

© 2017, David E. Giles

Read Some Econometrics this Month!

There are no April Fool's tricks in the following list of suggestions. 😐

• Antoine, B. and E. Renault, 2017. On the relevance of weaker instruments. Econometric Reviews, online.
• Golan, A. and A. Ullah, 2017. Interval estimation: An information theoretic approach. Econometric Reviews, online.
• Hendry, D. F. and P. C. B. Phillips, 2017. John Denis Sargan at the London School of Economics. Cowles Foundation Discussion Paper No. 2082, Yale University.
• Ozonur, D., H. T. K. Akdur, & H. Bayrak, 2016. Comparisons of tests of distributional assumption in Poisson regression model. Communications in Statistics - Simulation and Computation, online.
• Vijayamohanan, P. N., 2017. How do you interpret your regression coefficients? MPRA Paper No. 76867.
• Witmer, J., 2017. Bayes and MCMC for undergraduates. American Statistician, online.

© 2017, David E. Giles

Choosing Between the Logit and Probit Models

I've had quite a bit say about Logit and Probit models, and the Linear Probability Model (LPM), in various posts in recent years. (For instance, see here.) I'm not going to bore you by going over old ground again.

However, an important question came up recently in the comments section of one of those posts. Essentially, the question was, "How can I choose between the Logit and Probit models in practice?"

I responded to that question by referring to a study by Chen and Tsurumi (2010), and I think it's worth elaborating on that response here, rather than leaving the answer buried in the comments of an old post.

So, let's take a look.

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

ARDL Modelling in EViews 9

My previous posts relating to ARDL models (here and here) have drawn a lot of hits. So, it's great to see that EViews 9 (now in Beta release - see the details here) incorporates an ARDL modelling option, together with the associated "bounds testing".

This is a great feature, and I just know that it's going to be a "winner" for EViews.

It certainly deserves a post, so here goes!

First, it's important to note that although there was previously an EViews "add-in" for ARDL models (see here and here), this was quite limited in its capabilities. What's now available is a full-blown ARDL estimation option, together with bounds testing and an analysis of the long-run relationship between the variables being modelled.

Here, I'll take you through another example of ARDL modelling - this one involves the relationship between the retail price of gasoline, and the price of crude oil. More specifically, the crude oil price is for Canadian Par at Edmonton; and the gasoline price is that for the Canadian city of Vancouver. Although crude oil prices are recorded daily, the gasoline prices are available only weekly. So, the price data that we'll use are weekly (end-of-week), for the 4 January 2000 to 16 July 2013, inclusive.

The oil prices are measured in Candian dollars per cubic meter. The gasoline prices are in Canadian cents per litre, and they exclude taxes. Here's a plot of the raw data:

Do You Use P-Values and Confidence Intervals?

Unless your econometrics training has been true-blue Bayesian in nature, you'll have reported a lot of p-values, and constructed heaps of confidence intervals in your time.

Both of these concepts have been the centre of widespread controversy in the statistics literature since their inception. It's probably good to be aware of this - just so you don't go and "shoot yourself in the foot" at some stage.

Economist/econometrician Aris Spanos has published an interesting and readable piece about all of this In a recent issue of the journal, Ecology. His paper is titled, "Recurring Controversies About P Values and Confidence Intervals Revisited". You can read a summary on the Error Statistics blog, here.

I strongly recommend this paper.

© 2014, David E. Giles

The Deviance Information Criterion

A few years ago - twelve, to be specific - an interesting paper appeared in the Journal of the Royal Statistical Society. That paper, "Bayesian measures of model complexity and fit", by Spiegelhalter et al., stirred up a good deal of controversy within the statistical community. That much is apparent even from the "discussion" that accompanied its publication. More than 4,600 Google Scholar citations later, it continues to attract widespread attention - though not that much among econometricians, as far as I can tell. An exception is the paper by Berg et al. (2004).

In their 2002 paper, Spiegelhalter et al. introduced a new measure of model fit. They termed it the "Deviance Information Criterion" (DIC). Briefly, here's how it's defined:

The February Reading List

As always - there's lots of interesting reading out there. Here are my suggestions for this month:

• Advani, A. and Tymon Słoczyński, 2013. Mostly harmless simulations? On the internal validity of empirical Monte Carlo studies.Discussion Paper No. 7874, IZA, Bonn.
• Flaig, G., 2012. Why we should use high values for the smoothing parameter of the Hodrick-Prescott filter.  CESifo Working Paper No. 3816, Department of Economics, University of Munich.
• Kiviet, J. F. and J. Niemzczyk, 2013.  On the limiting and empirical distribution of IV estimators when some of the instruments are actually endogenous. EGC Report No: 2013/11, Nanyang Techological University.
• Lütkepohl, H., A. Staszewska-Bystrova, and P. Winker, 2014. Confidence bands for impulse responses: Bonferroni versus Wald. (Updated.) SFB 649 Discussion Paper 2014-007.
• Lv, J. and J. S. Liu, 2013. Model selection principles in misspecified models. Journal of the Royal Statistical Society, B, 76, 141-167. 
• Skeels, C. L. and L. W. Taylor, 2013. Prediction after estimation. Economics Letters, 122, 420-422.
• Tserkezos, K., 2013. Temporal aggregation and Ramsey's (RESET) test for functional form: Results from empirical and Monte Carlo experiment. Mimeo., Department of Economics, University of Crete.

© 2014, David E. Giles

Testing Up, or Testing Down?

Students are told that if you're going to go in for sequential testing, when determining the specification of a model, then the sequence that you follow should be "from the general to the specific". That is, you should start off with a "large" model, and then simplify it - not vice versa.

At least, I hope this is what they're told!

But are they told why they should "test down", rather than "test up"? Judging by some of the things I read and hear, I think the answer to the last question is "no"!

The "general-to-specific" modelling strategy is usually attributed to David Hendry, and an accessible overview of the associated literature is provided by Campos et al. (2005).

Let's take a look at just one aspect of this important topic. 

Information Criteria Unveiled

Most of you will have used, or at least encountered, various "information criteria" when estimating a regression model, an ARIMA model, or a VAR model. These criteria provide us with a way of comparing alternative model specifications, and selecting between them. 

They're not test statistics. Rather, they're minus twice the maximized value of the underlying log-likelihood function, adjusted by a "penalty factor" that depends on the number of parameters being estimated. The more parameters, the more complicated is the model, and the greater the penalty factor. For a given level of "fit", a more parsimonious model is rewarded more than a more complex model. Changing the exact form of the penalty factor gives rise to a different information criterion.

However, did you ever stop to ask "why are these called information criteria?" Did you realize that these criteria - which are, after all, statistics - have different properties when it comes to the probability that they will select the correct model specification? In this respect, they are typically biased, and some of them are even inconsistent.

This sounds like something that's worth knowing more about!

My "Must Read" List

I have to confess that the number of items on my list of papers that I really must read (very soon) is rather large. My excuse is the same as everyone else's - too many papers, too little time. However, here's a small selection of of some of the papers that I've added to that list recently:

Information and Entropy Econometrics

The eminent physicist Ed. Jaynes (1957a) wrote:

"Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum entropy estimate. It is least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information."

In other words, when we want to describe noisy data with a statistical model, we should always choose the one that has Maximum Entropy.

"An Information Theoretic Approach to Econometrics"

George Judge & Ron Mittelhammer have a new book, hot off the press: An Information Theoretic Approach to Econometrics (CUP, 2012).