Reading Suggestions for June

Well, here we are - it's June already.

Here are my reading suggestions:

• Abadie, A., S. Athey, G. Imbens, & J. Wooldridge, 2017. When should you adjust standard errors for clustering? Mimeo.
• Berk, R., A. Buja, L. Brown, E. George, A. K. Kuchibhotla, W. Su, & L, Shazo, 2019. Assumption lean regression. American Statistician, in press.
• Ghosh, T., M. Ghosh, & T. Kubokawa, 2019. On the loss robustness of least-square estimators, American Statistician, in press.
• Gustafsson, O. & P. Stockhammar, 2019. Variance stabilizing filters. Communications in Statistics - Theory and Methods, in press.
• Kocherlakota, N. R., 2019. A near-exact finite sample theory for an instrumental variable estimator. Mimeo. (Hat-tip to Frank Diebold.)
• Panagiotelis, A., G. Anathasopoulos, R. J. Hyndman, B. Jiang, & F. Vahid, 2019. Macroeconomic forecasting for Australia using a large number of predictors. International Journal of Forecasting, 35, 613-633.

© 2019, David E. Giles

A Permutation Test Regression Example

In a post last week I talked a bit about Permutation (Randomization) tests, and how they differ from the (classical parametric) testing procedure that we generally use in econometrics. I'm going to assume that you've read that post.

(There may be a snap quiz at some point!)

I promised that I'd provide a regression-based example. After all, the two examples that I went through in that previous post were designed to expose the fundamentals of permutation/randomization testing. They really didn't have much "econometric content".

In what follows I'll use the terms "permutation test" and "randomization test" interchangeably.

What we'll do here is to take a look at a simple regression model and see how we could use a randomization test to see if there is a linear relationship between a regressor variable, x, and the dependent variable, y. Notice that I said a "simple regression" model. That means that there's just the one regressor (apart from an intercept). Multiple regression models raise all sorts of issues for permutation tests, and we'll get to that in due course.

There are several things that we're going to see here:

1. How to construct a randomization test of the hypothesis that the regression slope coefficient is zero.
2. A demonstration that the permutation test is "exact". That it, its significance level is exactly what we assign it to be.
3. A comparison between a permutation test and the usual t-test for this problem.
4. A demonstration that the permutation test remains "exact", even when the regression model is mi-specified by fitting it through the origin.
5. A comparison of the powers of the randomization test and the t-test under this model mis-specification.

Dummy Variables in a Semilogarithmic Regression: Exact Distributional Results

For better or worse, semilogarithmic regression models are used a lot in empirical economics. 

It would be nice to think that this is because the researcher found that a logarithmic transformation of the model's dependent variable led to residuals that were more "normally" distributed than without the transformation. Unfortunately, however, it's often just "for convenience". With this transformation, the estimates of the regression coefficients have a simple interpretation, as explained below

I hate it when the latter situation arises. I've long since lost track of the number of times I've been at a seminar where the speaker has used this "simple interpretation" as an excuse for their choice of a semilogarithmic regression specification. For goodness sake, the choice of the model's functional form should be based on more than "convenience"!

For some of my previous comments about this point, see this post.

Most of you will know that when our semilogarithmic model includes a dummy (zero-one) regressor, we have to be careful about how we interpret that regressor's estimated coefficient. Suppose that we have the following regression model, where D is a dummy variable, and the X's are regresssors that are measured "continuously"

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

Note that there's no loss of generality here in having just one dummy variable in the model.

Then, the interpretation of the regression coefficients is:

1. A one-unit change in X_j leads to a proportional change of  γ_j (or a percentage change of 100γ_j) in y.
2. When the dummy variable changes from D = 0 to D = 1, the proportional change in y is [exp(β) -1]. Conversely, going from D = 1 to D = 0 implies a proportional change in y of  [exp(-β) -1]. Again, multiply by 100 to get a percentage change.

See Halvorsen and Palmquist (1980) for an explanation of the second of these results, and my comments in this earlier post.

Kennedy (1981) and Giles (1982) discuss the issue of estimating this proportional change in the case of the dummy variable. Their results relate to point estimation - with a focus on unbiased estimation of the proportional change, when the model's errors are normally distributed..

But what about interval estimation of this effect? 

April Reading

Very belatedly, here is my list of suggested reading for April:

• Biørn, E., 2017. Identification, instruments, omitted variables, and rudimentary models: Fallacies in the "experimental approach" to econometrics. Memorandum No. 13/2017, Department of Economics, Oslo University.
• Chambers, M. J., and M. Kyriacou, 2018. Jackknife bias reduction in the presence of a near-unit root. Econometrics, 6, 11.
• Derryberry, D., K. Aho, J. Edwards, and T. Peterson, 2018. Model selection and regression t-statistics. American Statistician, in press.
• Mitchell, J., D. Robertson, and S. Wright, 2018. R² bounds for predictive models: What univariate properties tell us about multivariate predictability. Journal of Business and Economic Statistics, in press. (Free download here.)
• Parker, T., 2017. Finite-sample distributions of the Wald, likelihood ratio, and Lagrange multiplier test statistics in the classical linear model. Communications in Statistics - Theory and Methods, 46, 5195-5202.
• Troster, V., 2018. Testing Granger-causality in quantiles. Econometric Reviews, 37, 850-866.

© 2018, David E. Giles

ASA Symposium on Statistical Inference - Recorded Sessions

In October of last year, the American Statistical Association held a two-day Symposium on Statistical Inference in Bethesda, MD.

The symposium was sub-titled, Scientific Method for the 21st. Century: A World Beyond p < 0.05. That gives you some idea of what it was about.

The ASA has now released video recordings of several of the sessions at the symposium, and you can find them here.

The video sessions include:

"Why Is Eliminating P-Values So Hard? Reflections on Science and Statistics." (Steve Goodman)

"What Have We (Not) Learnt from Millions of Scientific Papers with P-Values?" (John Ioannidis)

"Understanding the Needs for Statistical Evidence of Decision-Makers in Medicine." (Madhu Mazumdar, Keren Osman, & Elizabeth Garrett-Mayer) 

"Statisticians: Sex Symbols, Liars, Both, or Neither?" (Christie Aschwanden, Laura Helmuth, & Aviva Hope Rutkin) 

"The Radical Prescription for Change." (Andrew Gelman, Marcia McNutt, & Xiao-Li Meng)

Closing Session: “Take the Mic”

The videos are stimulating and timely. I hope that you enjoy them.

© 2018, David E. Giles

June Reading List

Here are some suggestions for you:

• Ai, C. and E. C. Norton, 2003. Interaction terms in logit and probit models. Economics Letters, 80, 123-129.
• Hirschberg, J. and J. Lye, 2017. Inverting the indirect - the ellipse and the Boomerang: Visualizing the confidence intervals of the structural coefficient from two-stage least squares. Journal of Econometrics, in press.
• Kim, I. and S. Park, 2017. Likelihood ratio tests for multivariate normality. Communications in Statistics - Theory and Methods, in press.
• Knotek, E. S. and S. Zaman, 2017. Financial nowcasts and their usefulness in macroeconomic forecasting. Working Paper 17-02, Federal Reserve Bank of Cleveland.
• Marczak, M. and V. Goméz, 2017. Monthly US business cycle indicators: A new multivariate approach based on a band-pass filter. Empirical Economics, 52, 1379-1408.
• Sherwood, C. and D. W. Kwak, 2017. New insights into an old problem - enhancing student learning outcomes in an introductory statistics course. Applied Economics, in press.

© 2017, David E. Giles

Monte Carlo Simulation Basics, I: Historical Notes

Monte Carlo (MC) simulation provides us with a very powerful tool for solving all sorts of problems. In classical econometrics, we can use it to explore the properties of the estimators and tests that we use. More specifically, MC methods enable us to mimic (computationally) the sampling distributions of estimators and test statistics in situations that are of interest to us. In Bayesian econometrics we use this tool to actually construct the estimators themselves. I'll put the latter to one side in what follows.

Some Suggested Reading for October

For your enjoyment:

• Diebold, F. X. & M. Shin, 2016. Assessing point forecast accuracy by stochastic error distance. NBER Working Paper No.2516.
• Franses, P.H., 2016. Yet another look at MIDAS regression. Econometric Institute Report 2016-32.
• Hillier, G. & F. Martellosio, 2016. Exact properties of the maximum likelihood estimator in spatial autoregressive models. Discussion Paper DP 07/16, Department of Economics, University of Surrey.
• Li, L., M.J. Holmes, & B.S. Lee, 2016. The asymmetric relationship between executive earnings management and compensation: A panel threshold regression approach. Applied Economics, 48, 5525-5545. 
• Lütkepohl, H., A. Staszewska-Bystrova, & P. Winker, 2016. Calculating joint confidence bands for impulse response functions using highest density regions. MAGKS Joint Discussion Paper 16-2016.
• Segnon, M., R. Gupta, S. Bekiros, & M.E. Wohar, 2016. Forecasting U.S. GNP growth: The role of uncertainty. Working Paper 2016-67, Department of Economics, University of Pretoria.

© 2016, David E. Giles

April Reading

April 1 already - time to update your reading list. Here are some suggestions:

• Baek, Y. I., J. S. Cho, and P. C. B. Phillips, 2015. Testing linearity using power transforms of regressors. 2015-RWP79, Economic Research Institute, Yonsei University.
• Gol, A. and D. E. Giles, 2015. HotGimmer: Random information. Working paper.
• Herwartz, H., N. Klein, and C. Strumann, 2015. Modelling hospital admission and length of stay by means of generalized count data models. Journal of Applied Econometrics, in press.
• Kabaila, P., R. Mainzer, and D. Farchione, 2015. The impact of a Hausman pretest, applied to panel data, on the coverage probability of confidence intervals. Economics Letters, in press.
• Lyhagen, J. and S. Ekberg, 2015. Beating the VAR: Improving Swedish GDP forecasts using error and intercept corrections. Journal of Forecasting, in press.
• Nadarajah, S., 2015. On the computation of Gauss hypergeometric functions. The American Statistician, in press.\
• Zhang, X. and A. Ullah, 2015. Group model averaging for finite sample size. Working Paper, Department of Economics, University of California, Riverside.

© 2015, David E. Giles

Conference in Honour of Aman Ullah

Last weekend, a small conference was held to honour Aman Ullah, a Distinguished Professor in the Department of Economics at the University of California, Riverside. I was to have participated in this gathering, but regrettably those plans had to be curtailed.

You'll find the program for the conference here. Aman (wearing a jacket) is front and centre in the picture below:

Aman and I go back a long way, and I remember fondly a period of leave that I spent with him at Western University; and his extended visits to both Monash University and the University of Canterbury. Along the way we managed to co-edit a couple of books together, and to say that I've learned a lot from him would be a huge understatement.

The description "a gentleman and a scholar" sits as well with Aman as with anyone else I can think of.

Thank you, Aman, for your enormous contributions to our discipline, your good humour, and your friendship.

© 2015, David E. Giles