Tag Archives: Statistics & Econometrics

Ergodicity and the law of large numbers (wonkish) If n identical trials A occurs v times, and if n is very large, then v/n should be near the probability p of A …This is one form of the law of large numbers and serves as a basis for the intuitive notion of probability as a measure of relative frequencies … It is usual to read into the law of large numbers things which it definitely does not imply. If Peter and Paul toss a perfect coin 10 000 times, it is customary to expect that Peter will...

Is 0.999 … = 1? (wonkish) What is 0.999 …, really? Is it 1? Or is it some number infinitesimally less than 1? The right answer is to unmask the question. What is 0.999 …, really? It appears to refer to a kind of sum: .9 + + 0.09 + 0.009 + 0.0009 + … But what does that mean? That pesky ellipsis is the real problem. There can be no controversy about what it means to add up two, or three, or a hundred numbers. But infinitely many? That’s a different story. In the real world, you can never...

Statistics — a question of life and death In 1997, Christopher, the eleven-week-old child of a young lawyer named Sally Clark, died in his sleep: an apparent case of Sudden Infant Death Sybdrome (SIDS) … One year later, Sally’s second child, Harry, also died, aged just eight weeks. Sally was arrested and accused of killing the children. She was convicted of murdering them, and in 1999 was given a life sentence … Now … I want to show how a simple mistaken assumption led to incorrect...

A guide to econometrics 1. Thou shalt use common sense and economic theory. 2. Thou shalt ask the right question. 3. Thou shalt know the context. 4. Thou shalt inspect the data. 5. Thou shalt not worship complexity. 6. Thou shalt look long and hard at thy results. 7. Thou shalt beware the costs of data mining. 8. Thou shalt be willing to compromise. 9. Thou shalt not confuse statistical significance with substance. 10. Thou shalt confess in the presence of sensitivity.

Making sense of data — categorical models [embedded content] Great lecture by one of my favourite lecturers — Scott Page.

RCT — no guide to the future To see what RCTs show, let me define the Cartesian product of X2, X3, . . . , Xn by Z. What RCTs show is that there exists some z ∈ Z, such that if we have the world in state (x, z) ∈ X instead of (y, z) ∈ X, the world in the next period will be in state a ∈ X instead of state b ∈ X. This is like saying, other things being the same (that is, z), if you vaccinate people, in the next period, there will be no influenza. But if you do not vaccinate them, there will...

If the centuries-old struggle with the problem of finding an analytical definition of probability has produced only endless controversies between the various doctrines, it is, in my opinion, because too little attention has been paid to the singular notion of random. For the dialectical root, in fact, lies in this notion: probability is only an arithmetical aspect of it. Nicholas Georgescu-Roegen Modern probabilistic econometrics relies on the notion of probability. To at all be amenable...

Logistic regression (student stuff)  [embedded content] And in the video below (in Swedish) yours truly shows how to perform a logit regression using Gretl.[embedded content]

Against multiple regression analysis Distinguished social psychologist Richard E. Nisbett has a somewhat atypical aversion to multiple regression analysis . In his Intelligence and How to Get It (Norton 2011) he wrote (p. 17): Researchers often determine the individual’s contemporary IQ or IQ earlier in life, socioeconomic status of the family of origin, living circumstances when the individual was a child, number of siblings, whether the family had a library card, educational attainment...

There have been over four decades of econometric research on business cycles … The formalization has undeniably improved the scientific strength of business cycle measures … But the significance of the formalization becomes more difficult to identify when it is assessed from the applied perspective, especially when the success rate in ex-ante forecasts of recessions is used as a key criterion. The fact that the onset of the 2008 financial-crisis-triggered recession was predicted by only a...