October Reading

Here's my latest, and final, list of suggested reading:

• Bellego, C. and L-D. Pape, 2019. Dealing with the log of zero in regression models. CREST Working Paper No. 2019-13.
• Castle, J. L., J. A. Doornik, and D. F. Hendry, 2018. Selecting a model for forecasting. Department of Economics, University of Oxford, Discussion Paper 861.
• Gorajek, A., 2019. The well-meaning economist. Reserve Bank of Australia, Research Discussion Paper RDP 2019-08.
• Güriş, B., 2019. A new nonlinear unit root test with Fourier function. Communications in Statistics - Simulation and Computation, 48, 3056-3062.
• Maudlin, T., 2019. The why of the world. Review of The Book of Why: The New Science of Cause and Effect, by J. Pearl and D. Mackenzie. Boston Review.
• Qian, W., C. A. Rolling, G. Cheng, and Y. Yang, 2019. On the forecast combination puzzle. Econometrics, 7, 39. 

© 2019, David E. Giles

Clive Granger Special Issue

The recently published Volume 10, No. 1 issue of the European Journal of Pure and Applied Mathematics takes the form of a memorial issue for Clive Granger. You can find the Table of Contents here, and all of the articles can be downloaded freely.

This memorial issue is co-edited by Jennifer Castle and David Hendry. The contributed papers include ones that deal with Forecasting, Cointegration, Nonlinear Time Series, and Model Selection.

This is a fantastic collection of important survey-type papers that simply must read!

© 2019, David E. Giles

Interpreting Dummy Variable Coefficients After Non-Linear Transformations

Dummy variables - ones that take only the values zero and one - are commonly used as regressors in regression models. I've devoted several posts to discussing various aspects of such variables, notably here, but also here, here, and here.

When the regression model in question is linear, in both the variables and the parameters, the interpretation of coefficient of such a dummy variable is simple. Suppose that the model takes the form:

    y_i = α + β D_i + Σ_j γ_j X_ji + ε_i     ;     E(ε_i ) = 0   ;   i = 1, ...., n.                          (1)

The range of summation in the term on the right-hand side of (1) is from 1 to k, if there are k regressors in addition to the dummy variable, D. (There is no loss of generality in assuming a single dummy regressor in what follows, and no further distributional assumptions about the error term will be needed or used.)

As you'll know, if D_i = 0, then the intercept coefficient in (1) is just α; and it shifts to (α + β) if D_i = 1. It changes by an amount equal to β, and so does the predicted mean value of y. Conversely, this amount changes by -β  if D_i changes from 1 to 0. Estimating (1) by OLS will give us an estimate of the effect on y of D_i sw from 0 to 1 in value, or vice versa.

But a bit more on estimation issues below!


Another way of interpreting what is going on is to think about the growth rate in the expected value of y that is implied when D changes its value. Setting D_i = 0, and then D_i = 1, this growth rate is:

   g_01i = [ (α + β + Σ_j γ_j X_ji) - (α + Σ_j γ_j X_ji)] / (α + Σ_j γ_j X_ji) = [β /  (α + Σ_j γ_j X_ji)] ,

which you can multiply by 100 to convert it into a percentage rate of growth, if you wish. 

Note that this growth rate depends on the other parameters in the model, and also on the sample values for the other regressors. 

Conversely, when D changes in value from 1 to 0, this growth rate is different, namely:

   g_10i = - [β / (α + β + Σ_j γ_j X_ji)]                            (i = 1, ...., n).

In this fully linear model these growth rates offer a somewhat less appealing way of summarizing what is going on than does the amount of change in the expected value of y. The latter doesn't depend on the other parameters of the model, or on the sample values of the regressors.

However, this situation can change very quickly once we move to a regression model that is non-linear, either in the variables or in the parameters (or both). 

That's what I want to focus on in this post. 

Let's consider some interesting examples that involve common transformations of the dependent variable in a regression model. Apart from anything else, such transformations are often undertaken to make the assumption of a normally distributed error term more reasonable.

Econometrics Reading List for November

Some suggestions........

• Garcia, J. and D. E. Ramirez, 2017. The successive raising estimator and its relation with the ridge estimator. Communications in Statistics - Theory and Methods, 46, 11123-11142.
• Silva, I. R., 2017. On the correspondence between frequentist and Bayesian tests. Communications in Statistics - Theory and Methods, online.
• Steel, M. F. J., 2017. Model averaging and its use in economics. MPRA Paper No. 81568.
• Teräsvirta, T., 2017. Nonlinear models in macroeconometrics. CREATES Research Paper 2017-32.
• Witmer, J., 2017. Bayes and MCMC for undergraduates. American Statistician, 71, 259-274.
• Zimmerman, C., 2015. On the need for a replication journal. Federal Reserve Bank of St. Louis, Working Paper 2015-016A.

© 2017, David E. Giles

End-of-Year Reading

Wishing all readers a very special holiday season!

• Agiakloglou, C., and C. Agiropoulos, 2016. The balance between size and power in testing for linear association for two stationary AR(1) processes. Applied Economics Letters, 23, 230-234.
• Allen, D., M. McAleer, S. Peiris, and A. K. Singh, 2015. Nonlinear time series and neural-network models of exchange rates between the US dollar and major currencies. Discussion Paper No. 15-125/III, Tinbergen Institute.
• Basu, D., 2015. Asymptotic bias of OLS in the presence of reverse causality. Working Paper 2015-18, Department of Economics, University of Massachusetts, Amherst.
• Giles, D. E., 2005. Testing for a Santa Claus effect in growth cycles. Economics Letters, 87, 421-426.
• Kim, J., and I Choi, 2015. Unit roots in economic and financial time series: A re-evaluation based on enlightened judgement. MPRA Paper No. 68411.
• 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

Summer Reading List

While I'm at the lake, fishing, this is your big chance to get on with some reading.

There won't be a quiz, but I know that you'll thank me for this later on:

• Aberdie, A., S. Athey, G. W. Imbens, and J. Wooldridge, 2014. Finite population standard errors. Mimeo.
• Boero, G., J. Smith, and K. F. Wallis, 2014. The measurement and characteristics of professional forecasters' uncertainty. Journal of Applied Econometrics, in press.
• Liu, C-A., 2014. Distribution theory of the least squares averaging estimator. Journal of Econometrics, in press.
• Manzan, S., 2014. Forecasting the distribution of economic variables in a data-rich environment. Journal of Business and Economic Statistics, in press.
• Sanderson, E. and F. Windmeijer, 2014. A weak instrument F-test in linear IV models with multiple endogenous variables. Discussion Paper 14/644, Department of Economics, University of Bristol.
• Yang, Z., 2014. A general method for third-order bias and variance corrections on a nonlinear estimator. Journal of Econometrics, in press.

© 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:

Econometrics and "Big Data"

In this age of "big data" there's a whole new language that econometricians need to learn. Its origins are somewhat diverse - the fields of statistics, data-mining, machine learning, and that nebulous area called "data science".

What do you know about such things as:

• Decision trees 
• Support vector machines
• Neural nets 
• Deep learning
• Classification and regression trees
• Random forests
• Penalized regression (e.g., the lasso, lars, and elastic nets)
• Boosting
• Bagging
• Spike and slab regression?

Probably not enough!

If you want some motivation to rectify things, a recent paper by Hal Varian will do the trick. It's titled, "Big Data: New Tricks for Econometrics", and you can download it from here. Hal provides an extremely readable introduction to several of these topics.

He also offers a valuable piece of advice:

"I believe that these methods have a lot to offer and should be more widely known and used by economists. In fact, my standard advice to graduate students these days is 'go to the computer science department and take a class in machine learning'."

Interestingly, my son (a computer science grad.) "audited" my classes on Bayesian econometrics when he was taking machine learning courses. He assured me that this was worthwhile - and I think he meant it! Apparently there's the potential for synergies in both directions.

© 2013, David E. Giles

How Science (Econometrics?) is Really Done

If you tweet, you may be familiar with #OverlyHonestMethods. If not, this link to Popular Science will set you on the right track. As it says: "In 140 characters or less, the info that didn't get through peer review."

Here are some beauties that may strike an accord with certain applied econometricians:

• "Our results were non-significant at p > 0.05, but they're humdingers at p > 0.1"
• "Experiment was repeated until we had three statistically significant similar results and could discard the outliers"
• "We decided to use Technique Y because it's new and sexy, plus hot and cool. And because we could."
• "I can't send you the original data because I don't remember what my excel file names mean anymore."
• "Non-linear regression analysis was performed in Graph Pad Prism because SPSS is a nightmare."
• "We made a thorough comparison of all post-hoc tests while our statistician wasn't looking."
• "Our paper lacks post-2010 references as it's taken the co-authors that long to agree on where to submit the final draft."
• "If you pay close attention to our degrees-of-freedom you will realize we have no idea what test we actually ran."
• "Additional variables were not considered because everyone involved is tired of working on this paper."
• "We used jargon instead of plain English to prove that a decade of grad school and postdoc made us smart."

Oh yes!!!!

© 2013, David E. Giles

So Much Good Reading........

Here are my latest reading suggestions:

• Choi, I., 2013. Panel Cointegration. Working Paper, Department of Economics, Sogang University, Korea.
• Davidson, R. and J. G. MacKinnon, 2013. Bootstrap tests for overdentification in linear regression models. Economics Department Working Paper No. 1318, Queen's University.
• Deng, A., 2013. Understanding spurious regression in financial econometrics. Journal of Financial Econometrics, in press.
• Feng, C., H. Wang, Y. Han, and Y. Xia, 2013. The mean value theorem and Taylor's expansion in statistics. The American Statistician, in press.
• Kiviet, J. F. and G. D. A. Phillips, 2013. Improved variance estimation of maximum likelihood estimation in stable first-order dynamic regression models. EGC Report No. 2012/06, Division of Economics, Nanyang Technical University.
• Lanne, M., M. Meitz, and P. Saikkonen, 2013. Testing for linear and nonlinear predicatability of stock returns. Journal of Financial Econometrics, 11, 682-705.

© 2013, David E. Giles

Simulating Critical Values for Some Test Statistics

This post comes at the request of Francesca, in a comment on an earlier post on Monte Carlo simulation.

The request was for some examples of how we can compute finite-sample critical values for different test statistics.  What this really means is that we want to simulate particular "quantiles" (points on the X-axis) for the distribution of the statistic.

Let's see what we can do about this. First, some background information.

Robust Standard Errors for Nonlinear Models

André Richter wrote to me from Germany, commenting on the reporting of robust standard errors in the context of nonlinear models such as Logit and Probit. He said he 'd been led to believe that this doesn't make much sense. I told him that I agree, and that this is another of my "pet peeves"!

Yes, I do get grumpy about some of the things I see so-called "applied econometricians" doing all of the time. For instance, see my Gripe of the Day post back in 2011. Sometimes I feel as if I could produce a post with that title almost every day!

Anyway, let's get back to André's point.