W HEN the surface of the economist is 14/1 7 scratched we generally find a belief that vertical integration in the corporate sector has increased during the past few decades, if not longer. This proposition, however, has not been put to a rigorous empirical test for the entire corporate sector. According to Professor Bain, We must, in the present state of knowledge, confine ourselves to a few remarks based on miscellaneous scraps of evidence. I In this note a measure of vertical integration in the corporate sector is developed. The measure is calculated for the year 1929 and for the period 1948 through 1965. The conclusion reached on the basis of this empirical evidence is that there has not been any discernible increase in the degree of vertical integration in the corporate sector. If anything, there might have been a slight decline. The index we use is the ratio of corporate sales to gross corporate product standardized to abstract from the changes in output mix. A rise in this index implies a decline in corporate vertical integration and vice versa.2 Because industry sales data are on a consolidated basis by corporation and most of the gross corporate product is on an establishment basis, this series reflects a preponderance of any general movements on the part of corporations to merge with suppliers or customers. If, for example, firm A has a gross corporate product of 500 and sales to firm B of 1000 (firm A's purchased material inputs are 500) and firm B has a gross corporate product of 500 and sales of 1500, then total corporate sales for both firms equal 2500 and total gross corporate product equals 1000. In this instance the ratio of sales to gross corporate product equals 2.5. If these two firms merge, total corporate sales will then be 1500 and gross corporate product will still be 1000. The new ratio of corporate sales to gross corporate product will be 1.5. Vertical integration has caused a decline in our ratio. As is readily aDDarent. neither pure horizontal integration nor a pure conglomerate movement will affect our ratio.3 There are natural differences among industries which preclude the meaningfulness of comparing the degree of vertical integration in one industry with that of any other industry. Thus a corporation in the service or mining industry will naturally have a much lower sales to gross corporate product ratio than a corporation in the retail or wholesale trade industry. If the proportional mix of total gross product is changing, we could very easily find a change in the aggregate sales to gross product ratio without any changes in this ratio for any specific industry. Any conclusions about changes in the ratio which are due to such changes in the proportional mix implies interindustry comparisons. In order to avoid the mix problem we calculate the aggregate ratio using the proportional mix of one base period. More explicitly our methodology is as follows: For any year t, total corporate sales, St, is equal to the sum of total corporate sales for each industry i. Thus,

IN a previous article with Professor Harold Watts, the authors demonstrated empirically the loss of information in the parameter estimators when data are aggregated prior to computing least-squares regressions [3]. These results came from simulations with a simple economic model containing identical microcomponents. Specifically, in addition to the error term, each component spent 0.9 of its previous income and 0.2 of its cash balance. The main point of our previous paper was that estimation prior to yielded substantially greater precision in the estimates of the parameters and their standard errors than did estimation of the same parameters after aggregation. The implications of this for hypothesis testing and the development of satisfactory policy response models seemed obvious. On the basis of a variety of evidence, including the paper with Watts and a paper by Orcutt [4], the case for seeking and frequently using disaggregated data seemed strong but one nagging concern remained. Suppose, as seems likely, the microcomponents exhibit different behaviors. In this case it might not be sensible to pool the data and treat it as a single sample from a single universe. However, if estimators from each micro equation are computed separately, would it still be desirable to use disaggregated data instead of data aggregated over all components? This turned out to be the case with identical components but would it be with nonidentical components in which something more than constant terms were different? This paper copes directly with this issue, and we demonstrate the importance of using disaggregated data even when microcomponents exhibit different behaviors. We do not deal with cases where microcomponents have nonlinear relations, but the need for disaggregated data in such cases seems fairly obvious without Monte Carlo experiments. If we wish to compare the accuracy of estimation at different levels of aggregation, we need a measure of merit different from the extent of bias and variance of parameter estimators, which we used in our previous study, because in an aggregate model whose components have different behaviors, the expected values of the estimators may be meaningless or nonstationary [Zellner, pp. 3-5]. Therefore, we use the accuracy of the out-of-sample forecasts to measure the merit of the estimated equations. In particular, we forecast the aggregate expenditure for the eight time periods following the last sample period. The rootmean-square forecast errors from models based on data at different levels of provide the yardstick for comparisons. Our results suggest that models estimated from micro data will give generally superior out-of-sample forecasts. This finding is at variance with the belief that one reaps an aggregation by aggregating the micro data prior to estimation. The concept of a possible gain was formalized in a 1960 article in this Review by Grunfeld and Griliches: