Causal Conjecture

Abstract

Causal relations are regularities in the way Nature's predictions change. Since we usually do not stand in Nature's shoes, we usually do not observe these dynamic regularities directly. But we sometimes observe statistical regularities that are most easily explained by hypothesizing such dynamic regularities. In this chapter, I illustrate this process of causal conjecture with a few simple examples. I first consider a negative causal relation: causal uncorrelatedness. Two variables are causally uncorrelated if there are no steps in Nature's event tree that change them both in expected value. They have, in this sense, no common causes. This implies, as we shall see, that the two variables are uncorrelated in the classical sense in every situation in the tree. When we observe that variables are uncorrelated in many different situations, then we may conjecture that this is due to their being causally uncorrelated. I will also discuss three causal relations of a positive character. These relations assert, each in a different way, that the causes (steps in Nature's tree) that affect a certain variable X also affect another variable Y. This implies regularities in certain classical statistical predictions. The first causal relation, which I call linear sign, implies regularity in linear regression. The second, scored sign, implies regularity in conditional