A Correspondence Principle for Simultaneous Equation Models - Fisher, Franklin M. (Econometrica, 1970)
Simultaneity as a LimitA well-known and highly convincing position on the nature of simultaneity in econometric models is that such models are only approximations to the true state of affairs.In fact, causation takes time, and the reactions given by the equations of the model truly occur not instantaneously but with a very small time lag.Unfortunately, however, data do not come to us sufficiently finely divided in time to allow us to observe such fastmoving reactions, so we take simultaneous instantaneously-holding relations as approximations, valid between the observations which nature allows us.Time lags are thus considered negligible provided they are sufficiently small.The consequences of this position for parameter estimation when observations occur at discrete points of time separated by an interval much larger than that in which the true reactions take place have been discussed 2 in the literature.In fact, however, this particular variant of the above view does not seem a very realistic one, We very seldom have observations on the value of a particular variable at precise discrete moments in time, 3 and, if we do, we seldom use the observations in that form.Much more common is the case in which the observations either by necessity or by choice are in the form of averages or sums over a non-zero time interval.Simultaneous This view has been discussed at length by Bentzel and Hansen [2].The basic position on causation has been vigorously maintained by H. Wold in several works, e.g., Wold and Jureen [11]. 2 Strotz [10]; but see also Gorman [6].