SEMAINE D ETUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 
44 
ables as instruments in the regressions for different endogenous 
variables in the same equation may result in a situation in 
which the longest lag involved in one such regression is greater 
than that involved in others. If data are only available from 
an initial date, this means that using the regressions as estim- 
ated involves eliminating some observations at the beginning 
of the period that would be retained if the longest-lagged instru- 
ment were dropped. In this case some balance must be struck 
between the gain in efficiency from extra observations and the 
loss from disregarding causal information if the lagged instru- 
ment in question is dropped. It is hard to give a precise guide 
as to how this should be done. (My personal preference would 
be for retaining the instrument in most cases.) Such circum 
stances will fortunately be relatively infrequent as the periods 
of data collection generally begin further back than those of 
estimation, at least in models of developed economies. Further, 
the reduction in available observations attendant on the use 
of an instrument with a large lag renders it unlikely that the 
introduction of that instrument adds significantly to correlation. 
Finally, the use of different instruments in the regressions 
replacing different endogenous variables in the equation to be 
estimated reintroduces the problem of inconsistency. When the 
equation to be estimated is rewritten with calculated values 
replacing some or all of the variables, the residual term includes 
not only the original structural disturbance but also a linear 
combination of the residuals from the regression equations used 
in such replacement. When the equation is then estimated by 
regressing the left-hand variable on the calculated right-hand 
ones and the instruments explicitly appearing, consistency re- 
quires not only zero correlation in the probability limit between 
the original disturbance and all the variables used in the final 
regression but also zero correlation in the probability limit 
between the residuals from the earlier-stage regression equa- 
tions and all such variables. If the same set of instruments 
is used when replacing every right-hand endogenous variable 
6] 
Fisher - pag. 57