Econometrics Beat: Dave Giles' Blog

Tuesday, October 1, 2013

Can Economists Forecast Crashes?

Without a doubt, Professor Sir David Hendry (University of Oxford) is one of the giants of econometrics. He's a wonderful speaker and champion of our profession, as you can see in this video, titled "Can Economists Forecast Crashes?"

Enjoy!

More on the Distribution of R-Squared

Some time ago, I had a post that discussed the fact that the usual coefficient of determination (R²) for a linear regression model is a sample statistic, and as such it has its own sampling distribution. Some of the characteristics of that sampling distribution were discussed in that earlier post.

You probably know already that we can manipulate the formula for calculating R², to show that it can be expressed as a simple function of the usual F-statistic that we use to test if all of the slope coefficients in the regression model are zero. This being the case, there are some interesting things that we can say about the behaviour of R², as a random variable, when the null hypothesis associated with that F-test is in fact true.

Let's explore this a little.

Solution to the Regression Trick

In a post earlier this month, I posed the following problem:

A researcher wishes to estimate the regression of y on X by OLS, but does not wish to include an intercept term in the model. Unfortunately, the only econometrics package available is one that "automatically" includes the intercept term. A colleague suggests that the following approach may be used to ‘trick’ the computer package into giving the desired result – namely a regression fitted through the origin:

“Enter each data point twice, once with the desired signs for the data, and then with the opposite signs. That is, the sample would involve ‘2n’ observations – the first ‘n’ of them would be of the form (y_i, x_i') and the next ‘n’ of them would be of the form (-y_i , -x_i'). Then fit the model (with the intercept) using all ‘2n’ observations, and the estimated slope coefficients will be the same as if the model had been fitted with just the first ‘n’ observations but no intercept.”

Is your colleague's suggestion going to work?

The answer is.....

Wednesday, September 25, 2013

Blogging About Your Research

Hat-tip to Arthur Charpentier for this link: "28 Reasons Why You Should Blog About Your Research".

New Working Paper

Yanan Li (a former graduate student) and I have just released a new Working Paper. It's titled, "Modelling Volatility Spillover Effects Between Developed Stock Markets and Developing Asian Stock Markets".

If you're interested, you can download a copy of the paper from here.

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Friday, September 20, 2013

Roger Farmer on the Natural Rate Hypothesis and the Phillips Curve

Following yesterday's post about the Phillips Curve, Roger Farmer kindly emailed me and drew my attention to some of his related work.

One of his articles appeared recently in the Bank of England's Quarterly Bulletin - see here. It's titled, "The Natural Rate Hypothesis: An Idea Past its Sell-By Date". The "quick summary" is as follows:

"Central banks throughout the world predict inflation with New Keynesian models where, after a shock, the unemployment rate returns to its so-called ‘natural rate’. That assumption is called the Natural Rate Hypothesis (NRH).

This paper reviews a body of work, published over the past decade, in which I argue that the NRH does not hold in the data and provide an alternative paradigm that explains why it does not hold.

I replace the NRH with the assumption that the animal spirits of investors are a fundamental of the economy that can be modelled by a ‘belief function’. I show how to operationalise that idea by constructing an empirical model that outperforms the New Keynesian Phillips Curve."

On p.246 of his article, Roger has a very nice illustrated summary of the estimation of the first Phillips Curve.

On Zero Correlation and Statistical Independence

I put the following material together yesterday in response to a request from one of our grad. students. I thought it might be helpful to some readers of the blog.

More on the History of the Phillips Curve

I've had two posts about A. W. (Bill) H. Phillips in the past - here and here. This is Phillips of the Phiilips Curve fame, of course.

Recently, Michael Mernagh has written two pieces about Phillips' original analysis for the online version of Significance Magazine, a joint publication of the American Statistical Association and the Royal Statistical Society. These pieces are titled A Short Overview of the Phillips Curve, and The Phillips Curve Revisited.

If you have an interest in the history of macroeconometrics, or the contributions of Bill Phillips, then Michael's short articles will interest you.

P-Values, Statistical Significance, and Logistic Regression

Yesterday, William M. Briggs ("Statistician to the Stars") posted on his blog a piece titled "How to Mislead With P-values: Logistic Regression Example".

Here are some extracts which, hopefully, will encourage to read the post:

"It’s too easy to generate “significant” answers which are anything but significant. Here’s yet more—how much do you need!—proof. The pictures below show how easy it is to falsely generate “significance” by the simple trick of adding “independent” or “control variables” to logistic regression models, something which everybody does...............

Logistic regression is a common method to identify whether exposure is “statistically significant”. .... (The) Idea is simple enough: data showing whether people have the malady or not and whether they were exposed or not is fed into the model. If the parameter associated with exposure has a wee p-value, then exposure is believed to be trouble.

So, given our assumption that the probability of having the malady is identical in both groups, a logistic regression fed data consonant with our assumption shouldn’t show wee p-values. And the model won’t, most of the time. But it can be fooled into doing so, and easily. Here’s how.

Not just exposed/not-exposed data is input to these models, but “controls” are, too; sometimes called “independent” or “control variables.” These are things which might affect the chance of developing the malady. Age, sex, weight or BMI, smoking status, prior medical history, education, and on and on. Indeed models which don’t use controls aren’t considered terribly scientific.

Let’s control for things in our model, using the same data consonant with probabilities (of having the malady) the same in both groups. The model should show the same non-statistically significant p-value for the exposure parameter, right? Well, it won’t. The p-value for exposure will on average become wee-er (yes, wee-er). Add in a second control and the exposure p-value becomes wee-er still. Keep going and eventually you have a “statistically significant” model which “proves” exposure’s evil effects. Nice, right?"

Oh yes - don't forget to read the responses/comments for this post, here.