MEMORANDUM

Now we have the curious situation that if the material at hand fulfills our
assumptions it is impossible to determine these constants a ij that express the nature
of our assumptions, because in this case we would only have a single observation,
namely, the one corresponding to the solution of the system. But if our assumptions
are not fulfilled, then it may be possible to determine what they constants a ij .
Suppose, for example, that the functions F 1 , F 2 ... contained also another set of
variables, ξ 1 ,ξ 2 ...ξ m , m being at least equal to 1. Our set of structural relations then
will take the form
F 1 (x 1 ,x 2 ,...x n , a 11 , a 12 ..., ξ 1 ,...ξ m ) = 0
F 2 (x 1 ,x 2 ,...x n , a 21 , a 22 ..., ξ 1 ,...ξ m ) = 0
. . . . . . . . . . . . . . . . . . . . .
F n (x 1 ,x 2 ,...x n , a n1 , a n2 ..., ξ 1 ,...ξ m ) = 0
Furthermore, let Ω(ξ 1 ,ξ 2 ...ξ m ) be the frequency distribution of the set
(ξ 1 ,ξ 2 ...ξ m ). Then to this frequency distribution of the set ξ there corresponds a
certain frequency distribution Π(x 1 ,...x n ) known from observation. We see that now
we really do get variations in the set (x 1 ,...x n ).
Now it is quite clear that the relation between the distribution Ω and the
distribution Π depends in a characteristic way on the magnitude of the parameters
a ij . Further, by expressing the fact that the x distribution deduced from the ξ
distribution (that is, from the function Ω) is identical with the actually observed x
distribution (that is, with the function Π), we obtain a system of equations in a ij
which will furnish a solution of the set a ij provided the equations in question are
theoretically and practically solvable.
Thus in point of principle, the constant a ij may be determined if we know Ω.
Actually, of course, we do not know Ω but we may make some more or less
plausible assumptions about it. To every such assumption corresponds a set a ij . In
an actual case, the formulae connecting Π and Ω would give an exact expression for
the effect of a change in the assumptions regarding Ω. Such a formula, it seems to
me will be of some value as a check on the perfectly gratuitous assumptions which
are sometimes made in this field.” (Frisch to Schumpeter, 13 December 1930).
Frisch’s letter thus foreshadowed an ingenious kind of probability approach to
Leontief’s problem. Leontief never got to see the letter from Frisch. When Frisch in 1933
published his Pitfalls essay with a sharp criticism of Leontief’s work it came without this
line of thought.
* * *
After advising Leontief with the applications Mordecai Ezekiel left for Berlin where
he took lessons to improve his German language. He visited Leontief’s parents several
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