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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - %¢ 
The first point we wish to illustrate is that all four rela- 
tions (71) and (73) make eo ipso predictors. It will be noted 
that in any BEID-system the expectational variables y ;; are 
linear expressions in the predetermined variables z,. Owing 
to the very simple structure of the model (71)-(74) the expecta- 
tional variable p; is in the present case nothing else than 
-P P,_1- As a consequence, the demand relation (71a) coin- 
cides with the supply relation (71b). This last feature illustra- 
tes how the reduced form may in the BEID-approach contain 
more information than the primary form. 
Another point for which the three models provide clearcut 
illustration is that once the stochastic structure of the model 
is specified the parameter estimation is technical matter and 
therefore, in principle, a noncontroversial problem. For eo ipso 
predictors least squares regression provides consistent estima- 
tes; hence, for example, when applied to time series data gen- 
erated from the stochastic process specified by (61)-(63) the 
regression of p, on d, will provide a consistent estimate for the 
coefficient — 0.8 in the demand relation (68a) of the PFUE- 
system, but in general not for the coefficient - 0.6/p in the 
demand relation (65a) of the ID-system. We see that if the 
least squares regression is applied to (65a) the bias may be 
quite substantial, depending on the numerical value of p, and 
that the least squares estimate will be unbiased only in the 
special case when p=0.75. 
3. PREDICTIVE TESTING OF NONEXPERIMENTAL MODELS (18) 
In the big arsenal of statistical methods, the techniques for 
the design and analysis of experiments are on the whole much 
more developed and refined than the techniques available for 
nonexperimental data. This is in particular so for the statistical 
*) The general argument of this section borrows from Ref. 34. 
., Wold - pag. 36