by From Lars Syll The impossibility of proper specification is true generally in regression analyses across the social sciences, whether we are looking at the factors affecting occupational status, voting behavior, etc. The problem is that as implied by the conditions for regression analyses to yield accurate, unbiased estimates, you need to investigate a phenomenon that has underlying mathematical regularities – and, moreover, you need to know what they are. Neither seems true. I have no reason to believe that the way in which multiple factors affect earnings, student achievement, and GNP have some underlying mathematical regularity across individuals or countries. More likely, each individual or country has a different function, and one that changes over time. Even if there was some
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from Lars Syll
The impossibility of proper specification is true generally in regression analyses across the social sciences, whether we are looking at the factors affecting occupational status, voting behavior, etc. The problem is that as implied by the conditions for regression analyses to yield accurate, unbiased estimates, you need to investigate a phenomenon that has underlying mathematical regularities – and, moreover, you need to know what they are. Neither seems true. I have no reason to believe that the way in which multiple factors affect earnings, student achievement, and GNP have some underlying mathematical regularity across individuals or countries. More likely, each individual or country has a different function, and one that changes over time. Even if there was some constancy, the processes are so complex that we have no idea of what the function looks like.
Researchers recognize that they do not know the true function and seem to treat, usually implicitly, their results as a good-enough approximation. But there is no basis for the belief that the results of what is run in practice is anything close to the underlying phenomenon, even if there is an underlying phenomenon. This just seems to be wishful thinking. Most regression analysis research doesn’t even pay lip service to theoretical regularities. But you can’t just regress anything you want and expect the results to approximate reality. And even when researchers take somewhat seriously the need to have an underlying theoretical framework – as they have, at least to some extent, in the examples of studies of earnings, educational achievement, and GNP that I have used to illustrate my argument – they are so far from the conditions necessary for proper specification that one can have no confidence in the validity of the results.
The theoretical conditions that have to be fulfilled for regression analysis and econometrics to really work are nowhere even closely met in reality. Making outlandish statistical assumptions do not provide a solid ground for doing relevant social science and economics. Although regression analysis and econometrics have become the most used quantitative methods in social sciences and economics today, it’s still a fact that the inferences made from them are — strictly seen — invalid.