Further manipulation permits the same conclusion if profitability is defined as profit as a percentage of sales. Since other measures of profitability, return on equity or on assets, are closely correlated with the return on sales, "it thus seems that profitability, no matter how measured, rises with P."20
There are forty-two observations potentially contained in the data in Table 2, a set of AS1, AS2, CR, PR1, PR2, NPF, OPPL, and AVAS for three time periods, 1952-1956, 1957-1961, and 1962-1965 for fourteen industries. The results of the regressions in Table 1, based upon the data pooled over the three time periods, rely upon thirty-six observations because measurement of all of these variables was not possible for every industry in each of the time periods. (See notes a, b, and c following Table 2).
To show the essential simplicity of what we mean by "determining the
direction of causality," we offer the following exercise. Set up two
linear equations in the two endogenous variables Y1 and Y2 with any
number (say K) of exogenous variables. Call the latter Z's. Assign
arbitrary numerical values, including zero, to the parameters of this
system (as from a telephone book, random number table, or the like).
As a simple example, the model at this point might look like the
Y1 = 6.0 + 2.0Z1 - 4.0Z2 + 3.5Z3 + 1.6Y2 Y2 = 0.8 - 4.4Z1 - 3.0Z2 + 7.1Z3 - 2.8Y1
None of these specifics is known to us, except the general form.
Now, either delete Y2 from the first equation or delete Y1 from the
second equation. The former makes the model one in which Y1 is
causally prior to Y2; the latter makes Y2 causally prior to Y1. Next,
make sure that at least one of the Es does not appear in the equation
from which the Y variable has been deleted, but does appear in the
other equation. These requirements result in a system of two equations:
one of them contains both Y's and as many as K Z's; and the other contains only one of the Y's and no more than K - 1 of the Z's. If Y1 and Z1 were deleted from the second equation, for example, the system
Y1 = 6.0 + 2.0Z1 - 4.0Z2 + 3.5Z3 + 1.6Y2 Y2 = 0.8 - 4.4Z1 + 7.1Z3