80 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
zation of a deterministic mode] brings the asymmetry in further re- 
lief; 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 hyper- 
inflations 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 
"21 
Wold - pag. 66