Knowledge that Transforms

This result does not mean that double-deflated real value added estimates should be accepted uncritically. For one thing, a double-deflated index is an external -that is, it is a weighted average involving some negative weights. This characteristic gives leverage to errors so that, for example, small percentage errors in the index of gross output appear as much larger percentage errors in real value added. Error arising from the use of a fixed weight linear approximation to the theoretically correct Divisia index is likely to grow more rapidly for a double deflated index than for an output index built up directly from input indexes.3 Also, double-deflation is invalid in the presence of technical change of most sorts. Because real value added is a residual in the double-deflation technique, the technique attributes all increase in output due to technical advance to value added. If the production function shifts with time according to

SINCE 1953, Congress has enacted several changes in the income tax laws which provide subsidies to investment. Depreciation rules were amended in 1954 to allow taxpayers to use various accelerated depreciation methods, such as sum of the years digits or double declining balance, as a substitute for straight line depreciation. In 1962 the tax laws were changed to shorten the lives over which assets could be depreciated, and to provide a tax credit on investment in equipment. The 1954 acceleration and the tax credit were suspended in 1966 and reimposed in 1967. Although these subsidies have been incorporated in many econometric and theoretical studies of investment behaviour, the latter have been concerned exclusively with the partial equilibrium impacts on investment and on the interaction between investment and income in a short-run Keynesian framework.' Partial equilibrium effects are certainly of interest and the use of these subsidies for countercyclical purposes has been emphasized by recent policy decisions. However it should be recalled that one of the major reasons for instituting these policies was to stimulate economic growth. Consequently in this paper an attempt is made to analyse in a general equilibrium context the long-run steady state implications of investment subsidies in general, and of the tax credit and of a change in depreciation methods in particular. Of course this method ignores all problems arising from cyclical fluctuations in aggregate demand.

HE major contention of this paper is that T American railroad investment behavior in the period 1897-1914 is best understood by emphasizing the role of financial factors, in spite of the fact that the accelerator theory from its inception has been most successfully applied to railroad investment in precisely this period [3, 11, 12]. (This was also true in Tinbergen (17) although Tinbergen preferred a model using profits as the explanatory variable.) This argument is also in direct contradiction to the recent explanation of railroad investment behavior in this period advanced by Kmenta and Williamson [10] . The argument rests upon significant changes in railroad finance which occurred at the beginning of the period. These permitted easier access to funds from sources external to the individual companies and likewise permitted more internal funds to be used for capital formation. This encouragement of investment due to easier financing was ended, however, by the Panic of 1907. These financial changes are sufficient to vitiate any form of the accelerator explanation of investment behavior which depends upon a fixed accelerator coefficient and a fixed lag structure of investment response to changes in demand for the period 1897-1914 as a whole. The argument is tested by comparing the effectiveness of alternative regression equations in explaining the investment behavior indicated by new estimates of railroad capital formation prepared for this study. Tihe new estimates are designed to remedy the defects existing in those published by Ulmer [18] . The results of the testing may be summarized most easily by reference to the Kmenta-Williamson hypothesis that investment behavior in American railroads is best explained by models appropriate to the various phases of the industry's life cycle. The model they chose to explain investment behavior in the phase 1897-1914 is described by the equation I = a, + a2 (RX.K_.) where I = net investment in 1929 dollars (Ulmer's estimates), X = output in 1929 dollars, and K = net capital stock (first of year). One conclusion of this paper is that this particular model is inferior to a model emphasizing the costs of financing investment. Of more general significance is the fact that models of investment behavior which incorporate financial variables and which have performed satisfactorily for more recent periods in the railroad and other industries also do quite well in the period 1897-1914. This disputes the notion that it is more efficacious to take separate phases of industry life cycles in order to explain investment behavior.

T HE use of aggregate production functions of the Cobb-Douglas type to explain the sources of growth, and of differences in growth rates, in recent years among eight European countries and the United States is discussed in this paper. Output is related to inputs of labor and capital, together with a residual not accounted for by these factor inputs, whether measured conventionally or in efficiency units. Until recently such procedures, when applied to European countries, required the use of balance-sheet data to measure capital, but our ignorance of prices and valuation methods implicit in such data has been a serious weakness. Thanks mainly to the enterprise of Simon Kuznets, Moses Abramovitz and their co-workers, supported by the Social Science Research Council, historical series on gross investment have recently become available for some European countries. For such countries the capital stock can now be estimated by cumulating investment expenditures in constant prices, along lines pioneered by Raymond Goldsmith for the United States. Despite uncertainties surrounding deflation procedures and the paucity of data for estimating useful lives, such capital estimates are, I believe, greatly to be preferred to figures resting on balance-sheet valuations. The availability of these new data prompted the present study, preliminary results of which are given in this paper.

HE most important motivation for T current study investigating lagged relationships in corporate demand for liquid assets is current controversy over lags in monetary policy. The literature is so wellknown that it need not be recapitulated here. The evidence that has been presented is of two kinds: analysis based on turning points in different series, i.e., that by Friedman; and an analysis based on estimation of distributed lag relationships, i.e., by Karaken and Solow. The latter authors estimate distributed lag relationships in different sectors and simply add these up. However, as Tucker [12] has pointed out, in a general equilibrium context summing lags in various sectors to measure lag in monetary policy is not a valid procedure. This implies that estimation of distributed lags should be done in a simultaneous equations context. But we feel that there are still several unresolved problems connected with estimation of single equations. The present study, therefore, concentrates on estimating distributed lags in a single equation context, with a specific view of analyzing merits and demerits of various alternative estimation techniques proposed till now for estimation of distributed lag models. We recognize that controversy over lags in monetary policy must be resolved in a general equilibrium context, with additional evidence on interactions among all variables, and especially on lags in each component function. For manufacturing corporations there is little evidence on lags in liquid asset demand, since most studies do not focus explicitly on this problem. Only Heston [7] and Anderson [2] enter lagged dependent variables in their regressions to examine adjustment. However, neither study discusses various problems of statistical estimation and interpretation. Anderson finds that approximately one-third of adjustment to equilibrium occurs in one quarter for cash while figure is about onefourth for government securities.' On other hand, Heston discovers that cash adjusts less than two-thirds of way to equilibrium in one year, and government securities less than one-half.2 The number of aggregate time-series studies of money demand dealing explicitly with lags is also not large, nor are statistical procedures particularly sophisticated. In one of earliest studies using a lagged model, Bronfenbrenner and Mayer [3] find that implied speed of adjustment toward equilibrium is onefourth to one-half per year. Treating money supply as an endogenous variable and using technique of two-stage least squares, Teigen [11] observes that during postwar period, one-third of adjustment to equilibrium occurs in a quarter, while for interwar period about one-half of adjustment takes place in a year.3 A study of money demand by Chow [4] also considers question of lagged adjustment at length, both by contrasting permanent income and wealth with current income and by including lagged dependent variables.4 Chow finds that speed of adjustment is less than one-half in first year. In a Federal Reserve study, De Leeuw [5] employs alternative estimation techniques in an attempt to deal with problems of serial correlation and lagged adjustment. He concludes his analysis saying the long lag hypothesis emerges from tests against post-war data