Fitting a model that has a parameter called ‘probability’ to data does not mean that the estimated value of that parameter estimates the probability of anything in the real world. Just as the map is not the territory, the model is not the phenomenon, and calling something ‘probability’ does not make it a probability, any […]
Statistics & Econometrics
In some fields—physics, geophysics, climate science, sensitivity analysis, and uncertainty quantification in particular—there is a popular impression that probabilities can be estimated in a ‘neutral’ or ‘automatic’ way by doing Monte Carlo simulations: just let the computer reveal the distribution … Setting aside other issues in numerical modeling, Monte Carlo simulation is a way to […]
Always, but always, plot your data. Remember that data quality is at least as important as data quantity. Always ask yourself, “Do these results make economic/common sense”? Check whether your “statistically significant” results are also “numerically/economically significant”. Be sure that you know exactly what assumptions are used/needed to obtain the results relating to the properties […]
While appeal to R squared is a common rhetorical device, it is a very tenuous connection to any plausible explanatory virtues for many reasons. Either it is meant to be merely a measure of predictability in a given data set or it is a measure of causal influence. In either case it does not tell […]
. Simpson’s paradox is an interesting paradox in itself, but it also highlights a deficiency in the traditional econometric approach towards causality. Say you have 1000 observations on men and an equal amount of observations on women applying for admission to university studies, and that 70% of men are admitted, but only 30% of women. […]
Unfortunately, social sciences’ hope that we can control simultaneously for a range of factors like education, labor force attachment, discrimination, and others is simply more wishful thinking. The problem is that the causal relations underlying such associations are so complex and so irregular that the mechanical process of regression analysis has no hope of unpacking […]
People sometimes speak as if random variables “behave” in a certain way, as if they have a life of their own. Thus “X is normally distributed”, “W follows a gamma”, “The underlying distribution behind y is binomial”, and so on. To behave is to act, to be caused, to react. Somehow, it is thought, these […]
Solve for x — give a single, unique number — in the following equation: x + y = 3. Of course, it cannot be done: under no rules of mathematics can a unique x be discovered; there are one too many unknowns. Nevertheless, someone holding to the subjective interpretation of probability could tell us, say, […]
Trygve Haavelmo — with the completion (in 1958) of the twenty-fifth volume of Econometrica — assessed the role of econometrics in the advancement of economics, and although mainly positive of the “repair work” and “clearing-up work” done, he also found some grounds for despair: We have found certain general principles which would seem to make good sense. Essentially, […]
As is brilliantly attested by the work of Pearl, an extensive and fruitful theory of causality can be erected upon the foundation of a Pearlian DAG. So, when we can assume that a certain DAG is indeed a Pearlian DAG representation of a system, we can apply that theory to further our causal understanding of […]