Sons, 1970.~~-10 runs is to see how well the model performs outside the sample period. Large RMS errors or large t-statistics generally indicate specification problems.Model builders, including ourselves, are inclined to "mine the data", i.e., to estimate a variety of different equation forms until one is found with acceptable error variance, (i.e., small) coefficient signs and t-statistics, Tests made outside the period of fit provide some insurance against this abuse of statistical theory (however compelling the procedure appears to be), although four data points by no means provide air-tight assurance.Chapter I, Ccont 'd) .
Model Simulation and the TROLL SystemEisner, M. Hairtial for the Troll System, Massachusetts Institute of Technology, 1969 (mimeographed) .Fromm, G. , and Taubman In what follows, we will be interested in two aspects of distributed lags.The firsfe'i^'-concerns the relation among alternative lag specifications and some of their statistical aspects, fffe^o ther concern is with ways of obtaining analytical insight into the dynamic properties 6«fr an already estimated relationship.In the real world we must deal with, there is never enough good qual- Notice that the smaller is k, the more rapidly the influence of past X's decays. Lagging (2. A) by one period and multiplying by k, we haveSubtracting (2.5) from (2.4), we have Further, we shall verify below that if k is between zero and one, a maintained change in X will cause Y to steadily approach its new equilibrium.The larger is k, the more important is past history, and the slower Y approaches equilibrium.We shall now examine parametSKs used to summarize lag distributions, and we shall evaluate these quantities for the Koyck lag structure.Clearly this structure is easily summarized by the parameter k, but the summary parameters we shall consider and (especially) the way we shall find them will be useful in the consideration of more complex lag structures.
Adjustment Time and Median LagIn equation (2.6), suppose that Y(0) = aX(0). That is, assume that the system is in equilibrium in period zero. Suppose X(l) = X(0) + 1, and that this value of X is maintained thereafter. Then Y(l) = a(l-k)and in general, summing the geometric series in k,The new equilibrium value of Y will be Y = Y(0) + ai^a s^agserted above.Notice that if k is between zero and one the difference between Y(t) and Y declines steadily over time, also as asserted above.The fraction of the adjustment to the new equilibrium completed after t periods is simplyThe median lag, T ,, is simply that value for t for which the fraction of adjustment completed equals one half. Thus we have T (2.8) .5=1 -k "'', or T^^= log (.5)/log (k) .Note that as k goes to zero, so does the median lag, as one might expect. where k is a non-negative integer.We now proceed to rewrite the general distributed lag equationhe second important concept, the lag polynomial, is represented here by the polynomial in brackets, P(L), in Equation (2.11). This equation has a variety of advantages over the e...