Tag Archives: Statistics & Econometrics

How do we attach probabilities to the real world? Econometricians usually think that the data generating process (DGP) always can be modelled properly using a probability measure. The argument is standardly based on the assumption that the right sampling procedure ensures there will always be an appropriate probability measure. But – as always – one really has to argue the case, and present warranted evidence that real-world features are correctly described...

Is ‘Cauchy logic’ applicable to economics? 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 have infinitely many heaps. What’s the numerical value of an infinite sum? It...

In order to make causal inferences from simple regression, it is now conventional to assume something like the setting in equation (1) … The equation makes very strong invariance assumptions, which cannot be tested from data on X and Y. (1) Y = a + bx + δ What happens without invariance? The answer will be obvious. If intervention changes the intercept a, the slope b, or the mean of the error distribution, the impact of the intervention becomes difficult to determine. If the variance of...

Although Bayesians think otherwise, to me there’s nothing magical about Bayes’ theorem. The important thing in science is for you to have strong evidence. If your evidence is strong, then applying Bayesian probability calculus is rather unproblematic. Otherwise — garbage in, garbage out. Applying Bayesian probability calculus to subjective beliefs founded on weak evidence is not a recipe for scientific akribi and progress. Neoclassical economics nowadays usually assumes that agents that...

In a recent issue of Real World Economics Review there was a rather interesting, if somewhat dense, article by Judea Pearl and Bryant Chen entitled Regression and Causation: A Critical Examination of Six Econometrics Textbooks … The paper appears to turn on a single dichotomy. The authors point out that there is a substantial difference between what they refer to as the “conditional-based expectation” and “interventionist-based expectation”. The first is given the notation: E[Y|X] While...

Econometrics — a Keynesian perspective It will be remembered that the seventy translators of the Septuagint were shut up in seventy separate rooms with the Hebrew text and brought out with them, when they emerged, seventy identical translations. Would the same miracle be vouchsafed if seventy multiple correlators were shut up with the same statistical material? And anyhow, I suppose, if each had a different economist perched on his a priori, that would make a difference to the outcome. J M...

Friedman on the limited value of econometrics Tinbergen’s results cannot be judged by ordinary tests of statistical significance. The reason is that the variables with which he winds up, the particular series measuring these variables, the leads and lags, and various other aspects of the equations besides the particular values of the parameters (which alone can be tested by the usual statistical technique) have been selected after an extensive process of trial and error because they yield...

Why Africa is so poor A few years ago, two economics professors, Quamrul Ashraf and Oded Galor, published a paper, “The ‘Out of Africa’ Hypothesis, Human Genetic Diversity, and Comparative Economic Development,” that drew inferences about poverty and genetics based on a statistical pattern … When the paper by Ashraf and Galor came out, I criticized it from a statistical perspective, questioning what I considered its overreach in making counterfactual causal claims … I argued (and continue...

Including all relevant material – good, bad, and indifferent – in meta-analysis admits the subjective judgments that meta-analysis was designed to avoid. Several problems arise in meta-analysis: regressions are often non -linear; effects are often multivariate rather than univariate; coverage can be restricted; bad studies may be included; the data summarised may not be homogeneous; grouping different causal factors may lead to meaningless estimates of effects; and the theory-directed...

Kocherlakota on picking p-values The word “significant” has a special place in the world of statistics, thanks to a test that researchers use to avoid jumping to conclusions from too little data. Suppose a researcher has what looks like an exciting result: She gave 30 kids a new kind of lunch, and they all got better grades than a control group that didn’t get the lunch. Before concluding that the lunch helped, she must ask the question: If it actually had no effect, how likely would I be...