Essential Fall Reading

• Buono, D., G. Kapetanios, M. Marcellino, G. Mazzi, & F. Papailias, 2018. Big data econometrics - Now casting and early estimates. Working paper N. 82, Baffi Carefin Centre for Applied Research on International Markets, Banking, Finance, and Regulation, Bocconi University.
• Fair, R. C., 2018. Information content of DSGE forecasts. Mimeo
• Lewbel, A., 2018. The identification zoo - Meanings of Identification. Forthcoming, Journal of Economic Literature.
• Pretis, F., J. J. Reade, & G. Sucarrat, 2018. Automated general-to-specific (GETS) regression modeling and indicator saturation for outliers and structural breaks. Journal of Statistical Software, 86, 3.
• Woodruff, R. S., 1971. A simple method for approximating the variance of a complicated estimate. Journal of the American Statistical Association, 66, 411-414.
• Zhang, R. & N. H. Chan, 2018. Portmanteau-type tests for unit-root and cointegration. Journal of Econometrics, in press.

© 2018, David E. Giles

Controlling My Heating Bill Using Bayesian Model Averaging

Where we live, in rural Ontario, we're not connected to "natural gas". Our home furnace runs on propane, and a local supplier sends a tanker to refill our propane tanks on a regular basis during the colder months.

Earlier this month we had to make a decision regarding our contract with the propane retailer. Should we opt for a delivery price that can vary, up or down, throughout the coming fall and winter; or should we "lock in" at a fixed delivery price for the period from October to May of next year?

Now, I must confess that my knowledge of the propane industry is slight, to say the least. I decided that a basic analysis of the historical propane price data might provide some insights to assist in making this decision. It also occurred to me, after doing this, that the analysis that I went through might be of interest to readers, as a simple exercise in forecasting using Bayesian model averaging.

Here are the details...........

September Reading List

This month's list of recommended reading includes an old piece by Milton Friedman that you may find interesting:

• Broman, K. W. & K. H. Woo, 2017. Data organization in spreadsheets. American Statistician, 72, 2-10.
• Friedman, M., 1937. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association, 32, 675-701.
• Goetz, T. & A. Hecq, 2018. Granger causality testing in mixed-frequency VARs with (possibly) cointegrated processes. MPRA Paper No. 87746.
• Güriş, B., 2018. A new nonlinear unit root test with Fourier function. Communications in Statistics - Simulation and Computation, in press.
• Honoré, B. E. & L. Hu, 2017. Poor (Wo)man's bootstrap. Econometrica, 85, 1277-1301. (Discussion paper version.)
• Peng, R. D., 2018. Advanced Statistical Computing. Electronic resource.

© 2018, David E. Giles

An Archival History of the Econometric Society

For those of you who have an interest in the history of Econometrics as a discipline - that's all of you, right (?) - there's a fascinating collection of material available at The Econometric Society: An Archival History.

As the name suggests, this repository relates to the Econometric Society and the journal Econometrica. It contains all sorts of fascinating facts, correspondence, and the like.

© 2018, David E. Giles

Recommended Reading

Here's my reading list for August:

• Ardia, D., K. Bluteau, & L. F. Hoogerheide, 2018. Methods for computing numerical standard errors: Review and application to value-at-risk estimation. Journal of Time Series Econometrics. Available online.
• Bauer, D. & A. Maynard, 2012. Persistence-robust surplus-lag Granger causality testing. Journal of Econometrics, 169. 293-300.
• David, H. A., 2009. A historical note on zero correlation and independence. American Statistician, 63, 185-186.
• Fisher, T. J. & M. W. Robbins, 2018. A cheap trick to improve the power of a conservative hypothesis tests. American Statistician. Available online.
• Granger, C. W. J., 2012. Useful conclusions from surprising results. Journal of Econometrics, 169, 142-146.
• Harville, D. A., 2014. The need for more emphasis on prediction: A 'nondenominational' model-based approach (with discussion). American Statistician, 68, 71-92.

© 2018, David E. Giles

Handbook of Quantile Regression

Quantile regression is a powerful and flexible technique that is widely used by econometricians and other applied statisticians. In modern terms we tend to date it back to the classic paper by Koenker and Bassett (1978).

Recently, I reviewed the Handbook of Quantile Regression. This edited volume comprises a number of important, original, contributions to the quantile regression literature. The various chapters cover a wide range of topics that extend the basic quantile regression set-up.

You can read my review of this book (Giles, 2018), here. I hope that it motivates you to explore this topic further.

References

Giles, D. E., 2018. Review of Handbook of Quantile Regression. Statistical Papers, 59, 849-850. 

Koenker, R., 2005. Quantile Regression. Cambridge University Press, Cambridge.

Koenker, R. and G. W. Bassett, 1978. Regression quantiles. Econometrica, 46, 33-50.

Koenker, R., V. Chernozhukov, H. Huming, & L. Peng (eds.), 2017. Handbook of Quantile Regression. Chapman & Hall/CRC, Boca Raton, FL.

© 2018, David E. Giles

What's in a Journal Name?

Back in 2011 I put together a very light-hearted working paper titled, What's in a (Journal) Name? Here's the associated link.

That paper addressed the (obviously) important question: "Is there a a correlation between the ranking of an economics journal and the length of the journal's title?"

I analyzed a sample of 159 academic economics journals. Although there was no significant association between journal quality and journal title length for the full sample of data, I did find that there was a significant “bathtub” relationship between these variables when the data were subjected to a rank correlation analysis over sub-samples. 

This led me to conclude (p.5),among other things:

'This “bathtub” relationship will undoubtedly sound alarm bells in the corridors of publishing houses as they assess proposals for new economics journals. The title, Economics, is no longer available, having been cunningly snapped up in recent years by an open-access, open-assessment e-journal which managed to “cover all of the bases” in one fell swoop. Even more recently the American Economics Association laid claim to the titles Macroeconomics and Microeconomics, albeit with an “AEA” prefix that they may wish to re-consider. The publishers of the journal, SERIEs: Journal of the Spanish Economic Association, which was launched in 2010, will no doubt ponder the merits of dropping the last six words of its title. However, there is hope. The title Econometrica has been spoken for since 1933, but to the best of our knowledge the more worldly journal title Econometrics is still available. Publishers should register their interest forthwith!'

As usual the latter remark proved to be safe advice on my part! I wonder if my subsequent invitation to join the Editorial Board of Econometrics was some sort of reward? 

I'll probably never know!

© 2018, David E. Giles

More on Regression Coefficient Interpretation

I get a lot of direct email requests from people wanting help/guidance/advice of various sorts about some aspect of econometrics or other. I like being able to help when I can, but these requests can lead to some pitfalls -  for both of us.

More on that in a moment. Meantime, today I got a question from a Ph.D student, "J", which was essentially the following:

" Suppose I have the following regression model

             log(y_i) = α + βX_i + ε_i    ;  i = 1, 2, ...., n .

How do interpret the (estimated) value of β?"

I think most of you will know that the answer is:

"If X changes by one unit, then y changes by (100*β)%".

If you didn't know this, then some trivial partial differentiation will confirm it. And after all, isn't partial differentiation something that grad. students in ECON should be good at?

Specifically,

      β = [∂log(y_i) / ∂X_i] = [∂logy_i / ∂y_i][∂y_i / ∂X_i] = [∂y_i  / ∂X_i] / y_i,

which is the proportional change in y for a unit change in X. Multiplying by 100 puts the answer into percentage terms.

So, I responded to "J" accordingly.

So far, so good.

But then I got a response:

"Actually, my model includes an interaction term, and really it looks like this:

    log(y_i) = α + βX_i + γ [X_iΔlog(Z_i)] + ε_i    ;  i = 1, 2, ...., n.

How do I interpret β?"

Whoa! That's not the question that was first asked - and now my previous answer (given in good faith) is totally wrong! 

Let's do some partial differentiation again, with this full model. We still have:

[∂log(y_i) / ∂X_i] = [∂logy_i / ∂y_i][∂y_i / ∂X_i] = [∂y_i  / ∂X_i] / y_i.

However, this expression now equals [β + γ Δlog(Z_i)].

So, a one unit change in X leads to a percentage change in y that's equal to 100*[β + γ Δlog(Z_i)]%.

This percentage change is no longer constant - it varies as Z takes on different sample values. If you wanted to report a single value you could evaluate the expression using the estimates for β and γ, and either the sample average, or sample median, value for Δlog(Z).

This illustrates one of the difficulties that I face sometimes. I try to respond to a question, but I really don't know if the question being asked is the appropriate one; or if it's been taken out of context; or if the information I'm given is complete or not.

If you're a grad. student, then discussing your question in person with your supervisor should be your first step!

© 2018, 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.

Some Reading Suggestions for July

Some summertime reading:

• Chen, T., DeJuan, J., & R. Tian, 2018. Distributions of GDP across versions of  the Penn World Tables: A functional data analysis approach. Economics Letters, in press. 
• Clements, K.W., H. Liu, & Y. Tarverdi, 2018. Alcohol consumption, censorship and misjudgment. Applied Economics, online
• Jin, H., S. Zhang, J. Zhang,& H. Hao, 2018. Modified tests for change points in variance in the possible presence of mean breaks. Journal of Statistical Computation and Simulation, online
• Pata, U.K., 2018. The Feldstein Horioka puzzle in E7 countries: Evidence from panel cointegration and asymmetric causality analysis. Journal of International Trade and Economic Development, online.
• Sen, A., 2018. A simple unit root testing methodology that does not require knowledge regarding the presence of a break. Communications in Statistics - Simulation and Computation, 47, 871-889.
• Wright, T., M. Klein, &K. Wieczorek, 2018. A primer on visualizations for comparing populations, including the issue of overlapping confidence intervals. American Statistician, online.

© 2018, David E. Giles