80 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -

zation of a deterministic mode] brings the asymmetry in further relief;
 in fact, as illustrated by (B;), in a stochastic specification of
the model the causal relations are expressed.in terms of predictors,
that is, conditional expectations, and conditional expectations always
are irreversible, and thereby asymmetric.

ALLAIS

To express myself more clearly may I comment briefly using
an example? I recently studied hyperinflations. My formulation
was a continuous one but for simplicity I used only monthly data.
It was therefore impossible to represent the last months of the hyperinflations
 correctly, and with monthly data the conclusion would
have been that the assumptions made were incorrect. But when
weekly data were considered the verification of the model was very
good and the hypothesis confirmed.
Thus my conclusion is that some models can introduce artificial
difficulties which could otherwise have been avoided.

WOoLD

Yes, this is surely an illuminating example to show that the
choice of time period is an important element in the specification
of hypotheses in a model. But it does not really bring home the
previous point about continuous time, for monthly data are discrete
in time, and so are weekly data. From the theory of stochastic
processes it is easy to give examples of problems that are easier to
handle in discrete time than in continuous time.

HAAVELMO

Let P(x, y, 8) be the joint probability law of the variables x
and y in the past, or under one kind of economic regime. fis a

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Wold - pag. 66