by Statistical inference — a self-imposed limitation The tool of statistical inference becomes available as the result of a self-imposed limitation of the universe of discourse. It is assumed that the available observations have been generated by a probability law or stochastic process about which some incomplete knowledge is available a priori … It should be kept in mind that the sharpness and power of these remarkable tools of inductive reasoning are bought by willingness to adopt a specification of the universe in a form suitable for mathematical analysis. Yes indeed — using statistics and econometrics to make inferences you have to make lots of (mathematical) tractability assumptions. Since econometrics aspires to explain things in terms of causes and effects it needs loads of assumptions, such as e.g. invariance, additivity and linearity. Limiting model assumptions in economic science always have to be closely examined since if we are going to be able to show that the mechanisms or causes that we isolate and handle in our models are stable in the sense that they do not change when we ‘export’ them to our ‘target systems,’ we have to be able to show that they do not only hold under ceteris paribus conditions. If not, they are of limited value to our explanations and predictions of real economic systems.
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Lars Pålsson Syll considers the following as important: Statistics & Econometrics
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Statistical inference — a self-imposed limitation
The tool of statistical inference becomes available as the result of a self-imposed limitation of the universe of discourse. It is assumed that the available observations have been generated by a probability law or stochastic process about which some incomplete knowledge is available a priori …
It should be kept in mind that the sharpness and power of these remarkable tools of inductive reasoning are bought by willingness to adopt a specification of the universe in a form suitable for mathematical analysis.
Yes indeed — using statistics and econometrics to make inferences you have to make lots of (mathematical) tractability assumptions. Since econometrics aspires to explain things in terms of causes and effects it needs loads of assumptions, such as e.g. invariance, additivity and linearity.
Limiting model assumptions in economic science always have to be closely examined since if we are going to be able to show that the mechanisms or causes that we isolate and handle in our models are stable in the sense that they do not change when we ‘export’ them to our ‘target systems,’ we have to be able to show that they do not only hold under ceteris paribus conditions. If not, they are of limited value to our explanations and predictions of real economic systems.
Unfortunately, real world social systems are usually not governed by stable causal mechanisms or capacities. The kinds of ‘laws’ and relations that econometrics has established, are laws and relations about entities in models that presuppose causal mechanisms being invariant, atomistic and additive. But — when causal mechanisms operate in the real world they mostly do it in ever-changing and unstable ways. If economic regularities obtain they do so as a rule only because we engineered them for that purpose. Outside man-made ‘nomological machines’ they are rare, or even non-existant.
So — if we want to explain and understand real-world economies we should perhaps be a little bit more cautious with using universe specifications ‘suitable for mathematical analysis’ …