Conditions of Inductive Study

Economic equations derived from experience, like Henry Schultz's demand curves for agricultural commodities, have, or strive to attain, this practical importance: they should make it possible to estimate the values which one of the variables, the ‘predictand’ (e.g., demand), will assume when other variables, the ‘predictors’ (e.g., income and price), are made to assume given values. There is, however, a proviso, silently admitted in this as in any other inductive work, whether quantitative or not. If we use the word ‘magnitude’ in a broad sense to include characteristics which can assume the values ‘presence’ or ‘absence’ but which cannot be measured; and if we use the words ‘observation period’ and ‘prediction period’ so as to include observations and predictions not only over time but, for example, within and between geographical areas (or any other samples), then we can formulate the proviso as follows.

Let y be the predictand, let x1, … xn be used by the investigator as predictors, and let a1, a2 … denote ‘all other magnitudes in the world’; some, but not all, of the a's enter the proposed relationship explicitly and are called its parameters. Then every a either must remain constant or its variations must have no significant influence on the value of y. This must be true both during the observation period and during the prediction period.

If the condition is not fulfilled during the observation period, the relationship between y and the x's is a ‘spurious’ one.