Diachronic correlation, process analysis and causal analysis

Conclusion

We have introduced three parameters of bivariate diachronic relation, viz.:

• 1) Constancy, measured as the area enclosed between the straight reference line and the empirical or idealized trajectory for one unit, the idealized trajectory for the case of more units. This is a measure of the over-all departure from the case of constant ratios between the rates of growth in the two variables, and the smaller the measure, the higher the constancy.

• 2) Regularity, measured as the diachronic correlation between X and Y around the idealized trajectory, whether based on one or more units. The measure will have to be based on correlation ratios if the variables are interval scale, in order to be sensitive to non-linear trajectories, in other words to low level of constancy.

• 3) Monotonicity, measured by counting the number of times the first derivative of the idealized trajectory, based on one or more units, changes signs. The higher the number, the lower the monotonicity.

  In addition we have introduced a measure that relates as much to synchronic relations as to diachronic relations:

• 4) Invariance, measured by counting the number of third variables relative to which the relation has been proved to be invariant. The higher the number, the more invariant the relation, but this measure makes best sense as a set-theoretical comparison between Irrel for one relation and Irrel for another relation.

Listed like this one sees clearly how limited a concept of causal relations based on maximum constancy, regularity, monotonicity and invariance is. One also sees how it has at all been possible to develop this concept on the basis of synchronic correlation: simply by assuming constancy and monotonicity over time, or by failing to notice these aspects of the relation. The focus has been on regularity, which has then been approached by means of synchronic correlation even though these correlations are often quite different from the corresponding diachronic correlations. Most of the emphasis has been on the condition of invariance, with completely unrealistic and hence rather uninteresting conditions for a relation to be referred to as causal.

But if we 1. introduce diachronic analysis and 2. relax these conditions, then more interesting conceptions on how social affairs can be studied develop. One might now construct a typology of sixteen types of relations depending on whether the four parameters above can be classified as high or low, but we shall not develop that scholastic exercise completely. Rather, it should be emphasized that the four are independent of each other so that all combinations are possible; and this can be used for a final definition:

In other words, we shall prefer to use the term “causality” when the diachronic relation is characterized by very high values of constancy, regularity and monotonicity, and divide them into universal and particular relations depending on whether they hold under a very wide or very narrow variety of conditions. The same distinction will also be used for processes, which in general are diachronic relations characterized by lower values of constancy, regularity and monotonicity. Of course, if all these values are very low, then there is no relation at all to speak of.