The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
MONTHLY StuineM evieu/ IN THIS ISSU E FEDERAL RESERVE BANK of CLEVELAND Changes in National Product Related to Selected Business Series......................2 Ownership of Demand Deposits............ 14 In order to estimate change in Gross National Product, it is possible to make computations from the combined changes registered in three current business series, which are identified on page 3. Resulting estimates are compared below with actual changes in GNP. B illio n s of do lla rs a n n u a l rate 500 400 300 Q U A R T E R L Y C H A N G E IN G R O S S N A T IO N A L P R O D U C T (magnified scale) Billions of dollars annual rate +20 Estim ate d ^ / +10 Changes In National Product Related to Selected Business Series Editor’s Note. The relationships between quar terly changes in Gross National Product and quarterly changes in certain selected business series, as described in this article, have been de veloped as an experiment. The purpose of the experiment, in its first phase, is to determine whether a few selected monthly business series, in combination, can be shown to have a record of reasonably close correlation with the behavior of GNP in terms of quarterly change. In general, this aim has been fulfilled, as will be seen below. The second phase of the experiment, which gives a broader meaning to the entire enterprise, concerns the possible usefulness of the relation ships portrayed here to the practical work of business analysis; many workers in this field are engaged periodically in estimating current stand ings of Gross National Product, before the official estimates for a given quarter have been an nounced, and often they make forecasts of GNP scores for one or more calendar quarters in ad vance. The extent to which the relationships out lined here may be found useful in estimation and forecasting cannot be definitely established at this time. In this respect, the experiment is inconclu sive, although some suggestions on the point are offered at the end of the article. Enough informa tion is provided in the article to enable the reader to share in the continuing phases of the experiment, by substituting newly observed values of the variables in the framework of the equations. 2 By use of the relationships described below, it is possible to combine the current (or pros pective) standings of a few familiar statistical series on current business activity, which are available with relative promptness, to give a reasonably close approximation of the current (or prospective) standings of the Gross Na tional Product. Such a procedure is not de signed to supplant the careful consideration of the behavior of the various component parts of GNP, as practiced by many re sponsible business analysts. Rather, it is de signed to supplement such analysis, with a view to the possibility of providing advance clues as to changes in the current or immedi ately prospective standing of GNP, prior to the official announcement of estimated figures for GNP and its constituent parts. The relationships have been developed by regression analysis, utilizing familiar meth ods of computation. By the adaptation of such methods to the electronic computer, which handles large quantities of detail in a short time, it has been possible to extend quite markedly the range of experimentation in the study of potentially useful relation ships. The chart on the cover of this issue shows the degree of closeness of one of the relation ships that has been found to be pertinent. After explaining this particular relationship, including the background of its development, attention will be turned to an alternative relationship, based on information drawn from a longer time span. First Equation For the first set of relationships, which is identified as “ Equation 1” , as well as in the case of other relationships discussed later, the statistical series which are selected to play the role of “ independent variables” are chosen principally on two counts: (1) their familiarity to business analysts, combined with relative promptness of availability of monthly information and (2) their usefulness in providing a clue, through statistical associ ation, to the changes in GNP. In connection with the first criterion, it is important to bear in mind that fairly good estimates of quar terly values of a given series may often be made on the basis of one or two months’ data. Such an estimation procedure has the sub stantial advantage of making full use of cur rent business series which are available on a monthly basis; official GNP estimates, as such, are available only on a quarterly or annual basis. Another basic point is that the relation ships between GNP and the respective busi ness series utilized here may work, and prob ably do work, in both directions. That is, the general course of the economy, as indicated by changes in GNP, has an influence upon the fortunes of the particular segments of the economy such as retail sales or inventory behavior, as well as the fortunes of the parts having an influence upon the whole. In the equations discussed below, Gross National Product, for statistical convenience, becomes the “ dependent” variable, while the familiar business series become “ independent” vari ables. So long as unwarranted conclusions of a cause-and-effect type are not read into the results, the procedure represents a defensible use of the correlation technique.(1) (i) Because of the way in which the variables are chosen, they are probably not stochastically independent of each other. The probable occurrence of multi-collinearity is not considered to invalidate the use of the relationship for the associative purpose here described. (For a note on a test of serial correlation of the residuals, which is a different type of consideration, see reference to the Durbin-Watson ratio in the “ Statistical Appendix” .) Equation 1 is as follows: X* = 1.1328 + 0.7165 X , + 0.6210 X 3 + 0.01495 X 4 Where: X i = Gross National Product X 2 = retail sales of durable goods stores X 3 = change in book value of manufac turers’ inventories X 4 = bank debits outside New York City All values are expressed in change from previ ous quarter (first differences) at seasonally adjusted annual rates, in billions of dollars. The relationship is based on the period from the first quarter of 1953 through the fourth quarter of 1959. Selection of Business Series Let us consider the variables which com prise the right-hand side of this equation. Retail sales of durable goods stores is a series which is well known for its sensitivity to cyclical changes, although, as is the case with almost any individual series, it exhibits its own peculiarities of behavior. The series em braces mainly the sales of autos and house hold goods, as measured by the sales of retail outlets dealing in such types of goods. It is a component part of the U. S. Department of Commerce’s well-known series on retail sales, expressed in dollars and available rea sonably promptly on a monthly seasonally adjusted basis. For the period 1953-59, the behavior of the durable-goods sales series shows a recogniza ble similarity to that of GNP itself; when combined with other series, to be described below, it plays a valuable part in assessing the changes in GNP through the association principle, for the period under consideration. Change in book value of manufacturers’ inventories is also based on a well-known De partment of Commerce series, available monthly on a seasonally adjusted basis. It should be distinguished from the inventory component of GNP accounting, which rep resents a somewhat different treatment of inventories and which is not available on a monthly basis. Manufacturers ’ inventories are known to be the most volatile (and, there3 GROSS NATIONAL PRODUCT and FIVE SELECTED VARIABLES Original series, quarterly values in annual rates K i l l ia n s o f d o l l a r s B i ll io n s o f d o l l a r s B illio n s of d o lla r s B illio n s of d o lla r s -1f 0/ ±J U i«d in Equation 2 . . . . . . . . . . . . U std in both Equation I and Equation 2 JV Used in Equation 1 All series are seasonally adjusted fore, a highly strategic) segment of the gen eral series known as “ business inventories” . It is essential to note that the change in manufacturers’ inventories, as compared with the change in the preceding quarter rather than the absolute level of inventories, repre sents the variable used in the equation, i.e., the inventory series enters the equation as “ change in change” . The latter concept is familiar to most business analysts. Bank debits outside New York City con stitutes a variable whose cyclical behavior has been found by numerous observers to have a high degree of correlation with that of GNP.(2) Bank debits in New York are ex cluded from the national totals because they are known to include episodic or random fluctuations of a financial nature, which de tract from the usefulness of the series as an indicator of general business activity. How ever, debits outside New York City, as a kind of broad measure of transactions, do tend to reflect changes in general business activity. The series is available monthly on a seasonally adjusted basis, as computed and published by the Board of Governors of the Federal Eeserve System. statistical tests may be used to measure the degree of closeness. Thus, the coefficient of multiple correlation is .9321.(3) The coefficient of determination is .8689, indicating that about 87 percent of the variation in GNP changes has been accounted for by the com bination of changes in the three named vari ables. The standard error of the estimate is ± $2.33 billion, indicating that in two-thirds of the cases an estimate based on the equa tion will differ from the actual value by an amount within a range of plus or minus $2.33 billion. (For additional detail, see Sta tistical Appendix.) These results are con sidered to throw a favorable light on the use of Equation 1 for determining an early approximation of GNP. It should be noted that all of the variables used in this analysis, including GNP, are in terms of dollar values unadjusted for price changes. Such a procedure is preferable to the use of estimated “ physical volume” series, mainly for practical reasons stemming from the obvious complexity, and probable arti ficiality, which would be involved in any attempt to deflate the various series' by estimations of price changes applying to the individual series. Interpreting the Results Rejection of Alternative Series When the variables which have just been identified are put to use in the proportions specified by Equation 1, the results are a series of estimates of quarterly changes in Gross National Product. A visual comparison of the estimated values with the actual values for the period from the first quarter of 1953 through the final quarter of 1960 is shown on the cover chart. (The equation was de rived from correlation analysis applying to 1953 through 1959. For the year 1960, the estimated values shown on the chart were obtained through use of the equation.) It is important to call attention to other business series which might have been used in the equation, but which were not used. In fact, a number of other series were subjected to experimentation in the sense that relation ships built upon them were run through com putations to determine coefficients of correla tion, standard error, etc. In some cases, such alternative series, which were finally rejected, were originally considered as substitutes for the independent variables previously de scribed; in other cases they were considered in the role of additional independent vari ables, thus bringing the number of such vari How close are the estimated values to the actual values in this instance? The usual (2) See, for example, John M. Firestone, Federal Receipts and Expenditures During Business Cycles, 1879-1958, a study by the National Bureau of Economic Research, Prince ton University Press, 1960, p. 56. (3) In evaluating the significance of such results, and the usefulness of the relationship as a practical device, it should be borne in mind that the variables are all expressed as first differences rather than as absolute values of the original series. For this type of correlation, a given standing of r or r2 is more significant than it would be for an absolutevalue series. 5 ables which would have been used in the multiple correlation to four or more.(4) What is, from some standpoints, the most interesting of the alternative variables con sidered and rejected is the series known as business expenditures for new plant and equipment. On a priori grounds this series would be considered a leading candidate. In fact, with a different time span (as described later) the series does emerge as a variable which should be utilized in order to obtain a significant relationship. Where the period concerned is 1953-1959, however, the “ plant and equipment expendi tures” series was found to be a harmful rather than a helpful member of the cast. The principal reason for such a finding is the marked lag of plant and equipment expendi tures (behind the general business cycle) in the turns to recovery in 1954 and 1958. (See the charts on page 4 showing the various series in original data form.) Whether or not the series should be generally considered a lagging series— a subject of some current de bate—the fact remains that at the troughs of recent cycles, but not at the peaks, there has been a marked tendency for it to lag; as a consequence, the timing of this series becomes off-beat in relation to the timing of other series. What will happen to the timing of this series in the setting of the current turn of the general business cycle is also a matter of considerable interest, although it is not a subject of the present study. A group of variables which was also con sidered and rejected was drawn from the operations of the Federal government. At first impression, one might wonder whether any set of relationships purporting to give a clue to the behavior of GNP would be satis factory if it did not include at least one factor taking account of the role of the Fed (4) Repeated experiment tended to fortify the conclusion that three well-chosen independent variables are sufficient to ac complish the task of approximation which has been under taken. Addition of a fourth or fifth independent variable appeared to yield no significant improvement. Such an out come appears to be similar to the experience encountered by other investigators who have recently concerned themselves with regression analyses of a somewhat parallel statistical nature. 6 eral government. But it will be seen that the lack of strict independence on the part of the variable on the right-hand side of the equa tion has some advantages in this connection. Each of the business series which has been selected for inclusion in the equation is quite clearly influenced by government activity; thus, the role of government has already been reflected to a considerable extent. As a consequence, the question of including variables which are drawn from government activity should be resolved, not on the basis of whether the government plays a significant role in economic activity (as it certainly does) but rather by a finding as to whether the inclusion of any particular government activity series would make for a closer rela tionship in the final result. While other in vestigators, under other circumstances, might come to a different conclusion, the experi ments performed in this particular study yield a negative result. That is, each of the government activity series which was tried experimentally had the effect of influencing the relationship toward either a poorer degree of correlation, or a better one to such a very slight extent that the addition of the variable has been deemed not worth while. Among the government series which were tested for such a purpose are the monthly series known as “ Cash Receipts from the Public” , “ Cash Payments to the Public” , and “ Excess of Receipts or Payments” . The series which comes closest to filling the bill for the purpose at hand is “ Cash Receipts” . Of all the readily available series on Federal government activity, the cash receipts series apparently has the strongest record of cor responding with business cycle fluctuations. (See Firestone, op cit.) But even in this case, the effects of the inclusion of that vari able do not justify its selection in terms of a sufficient improvement of the closeness of the relationship. Still another type of series which was ex amined was drawn from the international trade sector. The international sector, as is well known, represents a relatively small but significant part of GNP. The empirical tests applied to the inclusion of various series on exports, imports, or trade balance, however, resulted in the rejection of the candidates in volved. No serious consideration was given to the inclusion of any business series which tends to show a pattern of relatively uninterrupted growth, as distinct from cyclical fluctua tion. Thus, many series which are important segments of GNP are ruled out at the start, including those associated with consumer ex penditures for nondurable goods or services and those associated with state and local gov ernment outlays. The effects of such growth factors are reflected in consolidated form within the single “ plus” value which ap pears as a constant in the equation. (In Equation 1, that value is 1.1328 billion.) Relationship Drawn From Longer Time Span The relationship which has been discussed above is based upon a relatively short span of years. In light of the fact that use of any mathematical relationship based on closely associated historical data is of questionable accuracy for future computations to the ex tent that such associations become altered, a question naturally arises as to whether use of a longer time span might provide more reliable conclusions. With this point in mind, Equation 2 has been developed. This equation is drawn from historical relationships re vealed over the period from the first quarter of 1947 through the final quarter of 1959. The thirteen-year span virtually encompasses the entire postwar period to date. Equation 2 may be identified as follows: X t = 2.4158 + 0.8020 X 2 + 0.3230 X 3 + 0.0065 X 4 Where: X j = Gross National Product X 2 = plant and equipment expenditures X 3 = manufacturers’ sales X 4 = bank debits outside New York City All values are expressed in change from previ ous quarter at seasonally adjusted annual rates, in billions o f dollars. The relationship is based on the period from the first quarter of 1947 through the fourth quarter of 1959. Let us consider the variables which go into the right-hand side of this equation. One of the variables has been met as part of Equa tion 1, namely, bank debits outside New York City. It remains to explain why two of the variables used in Equation 1 are not used in Equation 2, and why two others have been substituted. ‘ ‘ Retail sales of durable goods stores ’ ’ turns out to be an unwise choice for the longer time span. The reason may be readily deduced. During the recession period of 1948-49, retail sales of consumer durables continued to march upward. (See the behavior of retail sales of durable goods stores in 1948-49 on the accompanying charts on page 4 which de pict the various business series here under discussion in their original data form.) The pent-up demand which had resulted from wartime deprivations had been far from fully satisfied at that time; that demand was one of the principal features of the early post war economic panorama. It is not surprising, therefore, that the degree of statistical rela tionship which was obtained through includ ing the consumer durables series over the longer time span failed to justify the inclu sion of that series. The case of plant and equipment expendi tures is, in some respects, the direct opposite of the consumer durables case. That is, in the early postwar period, plant and equipment expenditures performed in a way which was highly indicative of the general business cycle. It was in the trough phases of the more recent cycles, as noted earlier, that an off beat timing of this series is observable. The results of the correlation tests indicate that, despite the lag of plant and equipment ex penditures at certain turning points of recent years, the general performance of the series over the entire span of thirteen years justifies its inclusion as a variable in Equation 2. 7 The inclusion of manufacturers’ sales as a variable in Equation 2 in preference to “ change in book value of manufacturers’ in ventories” (as in Equation 1) also requires explanation. The broad considerations gov erning these two series, which from a prac tical standpoint are alternatives for inclu sion, are as follows: Any close examination of the behavior of “ manufacturers’ sales” and of “ change in manufacturers’ inven tories” shows that the two series are quite similar to each other, as well as to GNP, in their broad pattern of cyclical behavior. (This would be quite untrue, if the absolute value of manufacturers’ inventories were taken as the original series, rather than the change in inventories.) One reason why the two series are generally similar is that the manufac turers’ sales series reflects numerous inter industry transactions, where one firm’s sales often become another firm’s addition to in ventories. The practical question now becomes whether the “ manufacturers’ sales” series or the “ change in inventory” series is more appro priate for the purpose at hand. Through the use of correlation tests, it has been found that the “ change in inventories” series is better for inclusion in the short span (195359), while the “ sales” series works out better for the longer span involved in Equation 2. However, the differences are not large. Either series might have been used with plausibility for either equation; to use both, however, would represent undesirable duplication. It is difficult to assign any persuasive reason to the observed difference in behavior of these two series within the two contexts of time periods. No attempt to speculate on this point will be made here. For Equation 2, as was the case with Equa tion 1, various alternative series were con sidered and rejected. Both the Federal gov ernment type of series and the foreign trade type of series were considered and rejected for the reasons noted previously in connection with Equation 1. GNP CH ANGES ESTIMATED FROM THREE BUSINESS SERIES BY A RELATIONSHIP OVER A 13-YEAR PERIOD B illion s of d olla rs B illio n s of d o lla r s The three series used in this relationship I Equation 21 are as follow s: plant and equipment expenditures, m anufacturers' sales, bank debits outside N e w York City. 8 The degree of correlation found in Equa tion 2, although it appears to be the best that can be obtained through working with a limi ted number of variables for the thirteen-year period under consideration, is slightly less than the closeness of relationship found for Equation 1. Thus, for Equation 2, the coeffi cient of multiple correlation is .8804. The coefficient of determination is .7751, indicat ing that about 78 percent of the variation in GNP changes has been explained by the combination of changes in the three named variables. The standard error of the estimate is ± $2.84 billion, indicating that in twothirds of the cases an estimate based on the equation will differ from the actual value by an amount within a range of plus or minus $2.84 billion. (For additional detail, see Statistical Appendix.) The fact that the relationship is not as close for this longer-span equation as it was for the shorter may not be surprising. Insofar as the variables were selected to a large extent on their performance in giving a good fit, the shorter length of time involved in the first equation may have served to limit the prob lems of non-synchronous timing of individual series in particular cycles. At the same time, it seems possible that the longer-span rela tionship may have a greater “ durability” . Best of Both Worlds? In view of the differences between the two equations just noted, the question naturally arises as to whether a combination of the two relationships might be employed to advan tage. "Without attempting a formal consolida tion of the two equations, which might pre sent statistical complications beyond the level of suitability for this presentation, a simple arithmetic combination of the two procedures may be essayed on an ad hoc basis. Such an operation is illustrated in the accompanying table. Actual and estimated values for GNP changes, utilizing the relationship of Equa tion 1, are shown alongside the corresponding values obtained from the use of Equation 2, over an identical time span, i.e., 1953 through 1960. For each individual quarter, a mean of the two computed values is ascertained. By comparison with the actual values of GNP changes, the errors (residuals) are shown for each of the three sets of computations, i.e., those based on Equation 1, those based on Equation 2, and those based on the mean of the two results. An examination of the table indicates that the plus and minus residuals associated with the use of each of the two equations tend to offset each other, at least to some extent. The residuals resulting from the combined opera tion (as shown in the final column of the table) throw a favorable light upon the use of the joint relationship, insofar as it pro vides estimates which are slightly closer to actual values.(5) I f the combined method should be used in practice to estimate current or prospective changes in GNP, as the latter unfold in each succeeding quarter, the basic logic would be as follows: The advantage of possibly greater stability of the longer-run relationship would be, at least in part, re tained. The use of the shorter-span relation ship would give an additional “ weight” to more recent experience, which seems appro priate. If the reader should ask which of the three relationships is actually recommended for a try-out in practice (use of Equation 1 or of Equation 2 or of the combined results), a reply that the answer depends on circum stances may seem inadequate. At the least, it may be possible to sort out the circumstances. Thus, if the busy business analyst has a limited curiosity to try one of these pro cedures in the simplest possible form, as the business data of succeeding calendar quarters unfold, then he should probably select Equa tion 1. But if he is suspicious of the perform ance of the relationship described by Equa tion 1 and if he has a bit more time or patience for experimenting, it is suggested that he compute the values from both equa( 5) Thus, the standard error of estimate of the combined result is $2.25 billion, which is less than the 2.33 value for the standard error of the estimate for Equation 1, and less than the 2.84 value for the standard error of the estimate for Equation 2, as applying to the observations from 1953 to 1959. 9 ESTIMATES AND RESIDUALS Three Alternative Procedures (Annual rates, in billions of dollars) GNP Actual Change Equation 1 Equation 2 Estimate Residual Estimate Estimates 1 & 2 Combined Residual Mean Residual 1953 I II III IV + + — - 5.9 4.3 1.7 6.1 + 7.3 + 4.4 — .3 — 4.2 + 1.4 + .1 + 1.4 + 1.9 + + + — 6.5 4.8 4.1 4.2 + .6 + .5 + 5.8 + 1.9 + + + — 6.9 4.6 1.9 4.2 + 1.0 .3 + + 3.6 + 1.9 1954 I II III IV — — + + 1.0 1.1 3.1 8.8 + + + + 1.5 2.3 1.9 9.3 + 2.5 + 3.4 — 1.2 + .5 + + + + 2.4 1.5 3.5 3.9 + 3.4 + 2.6 + -4 — 4.9 + + + + 2.0 1.9 2.7 6.6 + 3.0 + 3.0 — .4 — 2.2 1955 I II III IV +13.5 + 8.7 +10.4 + 5.5 +10.3 +12.1 + 8.5 + 5.6 — 3.2 + 3.4 — 1.9 + .1 + 11.6 +10.7 + 8.9 + 6.8 — + — + 1.9 2.0 1.5 1.3 +11.0 +11.4 + 8.7 + 6.2 1956 I II III IV + + + + 1.7 4.4 6.0 9.0 + + + + 4.1 4.0 1.8 8.7 + 2.4 — .4 — 4.2 — .3 + 6.5 + 5.5 + 2.9 +10.9 + + — + 4.8 1.1 3.1 1.9 + + + + 1957 I II III IV + + + — 8.5 3.6 6.2 6.0 + + + — 6.4 1.1 3.9 6.3 — 2.1 — 2.5 — 2.3 — .3 + 7.7 — .2 + 4.9 — 5.4 1958 I II III IV —10.3 + 4.8 + 10.2 + 14.0 __ 8.7 + 2.8 + 7.7 +15.7 + — — + 1.6 2.0 2.5 1.7 1959 I II III IV + 12.1 + 14.8 — 6.5 + 5.0 +16.9 +11.5 — 3.9 + 3.3 + — + — 1960 I II III IV +14.9 + 3.7 — 1.5 — 0— + 6.7 + .2 — 5.1 + .7 10 _ 2.5 + 2.7 — 1.7 .7 + 5.3 4.8 2.4 9.8 + 3.6 .4 + — 3.6 .8 + — .8 — 3.8 — 1.3 + -6 + 7.1 .5 + + 4.4 — 5.9 — 1.4 — 3.1 — 1.8 + .1 — 9.1 + -6 + 8.5 + 10.9 + — — — _ 8.9 + 1.7 + 8.1 +13.3 + 1.4 — 3.1 — 2.1 — .7 4.8 3.3 2.6 1.7 + 10.9 + 15.6 + .4 + 2.5 — 1.2 + .8 + 6.9 — 2.5 +13.9 +13.6 — 1.8 + 2.9 + — + — _ 8.2 — 3.5 — 3.6 + .7 + 9.7 + 2.6 — .7 — 1.7 — 5.2 — 1.1 + .8 — 1.7 + 8.2 + 1.4 — 2.9 -- .5 _ 6.7 — 2.3 — 1.4 -- .5 1.2 4.2 1.7 3.1 1.8 1.2 4.7 2.1 tions, and then compute the mean of the two values as suggested by the combined method. In any event, the analyst should bring his general knowledge of the current economic situation to bear upon the choice of a final estimate or forecast. As stated at the outset, the devices described here are in tended, at most, to offer a supplement to, rather than a substitute for, other methods of estimating Gross National Product. The practical usefulness of any or all of the relationships discussed above will depend not only on the closeness of the particular relationship selected (and its stability) but also—and perhaps in even greater measure —upon the readiness with which the values for the business series on the right-hand side of the equation can be ascertained, estimated, or forecasted on a developing, current basis. Attention must now be given to this phase of the question. Problems In Estimating Individual Series The procedures herein outlined may be em ployed under two sets of circumstances which differ in respect to the boldness of the fore casting element involved in the project. Under one set of circumstances, the analyst finds himself, let us say, in early April to be confronted with the task of estimating GNP for the first calendar quarter of that year. The preliminary (earliest available) official estimates of first-quarter GNP will not arrive at his desk until late in April. Using Equa tion 1, as outlined above, the analyst will assemble the monthly data for changes in the three independent variables. He probably will have figures for all of the series as applying to the months of January and Feb ruary. He will make his estimates or guesses for the missing March data as required and then will assemble his partly known and partly estimated quarterly figures represent ing change from the previous quarter; he will then utilize the equation to compute his esti mated change for GNP for the first quarter. Whether this entire procedure should be termed “ estimation” or “ forecasting” is a matter of language. In any event, the fore casting element in this case is relatively modest. A different set of circumstances obtains when the analyst in early April, for example, is attempting to make an outright forecast of GNP for the second, third, and fourth quar ters of the given year. At this point, the ques tion naturally arises as to how ‘ *forecastable ’ ’ the individual series utilized in the equations may be considered to be. Some of the varia bles are more difficult to forecast than others. Among the three variables which were selected for Equation 2, for example, it seems clear that plant and equipment expenditures lends itself readily to forecasting. The familiar survey of business intentions to make expenditures for plant and equipment, as assembled and published by the U. S. De partment of Commerce and the Securities and Exchange Commission, is a great aid at this point; somewhat similar surveys pub lished by several private organizations are of significant supplementary value. Another one of the variables, which is used here in both equations, does not lend itself readily to forecasting, namely, bank debits outside New York City. There is little or noth ing by way of statistical resources which will provide a crutch for forecasters in respect to this series. The analyst, unless he is cautious, is apt to have his judgment on that variable influenced unduly by his over-all view of the future of the economy; in the given context, this becomes circular reasoning, which is, un fortunately, an all too familiar experience in the art of outlooking. Such a drawback at tributable to the bank debits series for the purpose at hand might result in the series being excluded from the equation, were it not for the fact of its outstanding statistical per formance in the matter of correlation with quarterly changes in GNP, and therefore its contribution to “ fit” . (See “ partial correla tion coefficients” in the Statistical Appendix.) The other variables utilized either in Equa tion 1 or Equation 2 fall somewhere between “ plant and equipment expenditures” and “ bank debits” in respect to ease or difficulty 11 of forecasting. In the case of retail sales of durable goods stores, there is a body of perti nent information on outlook which is avail able, although it is not always in the form desired. Thus, there are several well-known surveys of consumer intentions to spend for durable goods which throw a general, but usually indirect, light on the future course of that variable. In the case of change in book value of man ufacturers’ inventories, there is much current discussion among economists as to how the outlook for the series under a given set of circumstances is to be evaluated. Regression analyses, somewhat similar to that employed for GNP in this endeavor, have been brought to bear upon the behavior of business inven tories.< ) Manufacturers’ sales, as distinct 6 from “ manufacturers’ inventories” , consti tutes a series which perhaps deserves more analytical attention than it ordinarily re ceives. Preoccupation with inventory-sales ratios may have diverted attention from the behavior of “ manufacturers’ sales” as a series in its own right. As it now stands, there appear to be few, if any, mechanical aids which offer assistance toward outright fore casting of that particular series; data on (6) See “ Measures of Inventory Conditions” , by Nestor E. TerJeckyj and Alfred Telia, Technical Paper No. 8, National Industrial Conference Board, New York, 1960. (The equa tions developed in this study apply to total business inven tories rather than manufacturers’ inventories.) manufacturing output may be of some in direct help. Altogether, it may be concluded that the specific business series which are utilized in the relationships discussed in this article appear in a less favorable light from the standpoint of their predictability than they do from the standpoint of their ready avail ability on a current basis. The test of the usefulness of the entire procedure for estima tion or forecasting of GNP may turn about this point. For, if the analyst in practice is forced to turn to other material because of any blind side in respect to these particular variables, he may decide that the entire de vice is not worth the candle. The outcome remains to be seen. No useful end would be served by exaggerating the potentialities of what is, after all, a rather mechanical device in a field which is still governed more largely by art than by mathematics. A study which would be related to the pres ent one, and which would be interesting al though quite complex, would be an attempt to develop a regression analysis for GNP along the lines followed here, but with the amend ment that variables would be selected ex plicitly and measurably upon the basis of relative forecastability, as well as upon the basis of their ready availability and their con tribution to “ fit.” (The statistical appendix to this article appears on the facing page.) 12 STATISTICAL APPENDIX For Equation 1: For Equation 2: The multiple correlation coefficient = R 1.234 = .9321 Multiple correlation coefficient = Ri .234 = .8804 The coefficient of determination = R 2 = .8689 Coefficient of determination = R 2 = .7751 The standard error of estimate = S x = $2.3263 billion Standard error of estimate = Sx = $2.8428 billion The partial correlation coefficients are ri2.34 — .4764 ri3.24 = .5014 ri4.23 = .6712 The fi coefficients, based upon a standard ized expression of each independent vari able, reveal the effects of the individual variables, confirming the relative showings of the partial correlation coefficients, as follows: ^ 12.34 ~ .2680 ^ 13.24 = .2786 /® i4.23 =: .5183 The Durbin-Watson ratio for Equation 1 was found to be 2.18. This value being larger than the upper limit of the test ratio (for 28 observations and 3 independ ent variables) at both the 1% and 5% significance levels, we may conclude that the residuals are not serially correlated. Partial correlation coefficients = ri 2.34 = .2766 ri3.24 == .4907 ^ 4.23 — .2535 / coefficients are as follows: 3 /?12.34 ~ .1582 = ^13.24 ~ .5590 Pn.23 ~ .2536 The Durbin-Watson ratio, calculated as 1.57 for Equation 2, falls within the “ twi light zone” between the lower limit (1.43) and the upper limit (1.68) at the 5% significance level for 3 independent vari ables and 52 observations. Considering that a ratio greater than 1 .6 8 is required to in dicate absence of serial correlation of the residuals at the stated level of significance, it may be concluded that a slight tendency of such correlation may be present. How ever, it should be noted that the ratio falls nearer the upper limit than the lower limit of the “ twilight zone’ \ 13 Ownership of Demand Deposits (Fourth District) the volume and the ownership dis that the increase in the number of accounts tribution of privately held demand de was due mainly to the rise in the number of posits at insured commercial banks in the accounts held by individuals. The combina tion of a slight increase in the total number of Fourth District showed some effects of the turnaround in business activity which took accounts and a decline in the deposit volume resulted in a smaller average size of privately place in 1960. Hence, the volume of privately held accounts. held demand deposits declined, on a year-toyear basis for the period ended January 25, 1961, to the lowest level of the past three Ownership of Demand Deposits years, for the days of record. On January 25, DOLLAR VOLUME, BY TYPE OF OWNER 1961, such deposits amounted to an estimated Fourth District $8,229 million, which was down $447 million from the year-ago figure.(1) The decline was in contrast to a $187-million expansion which had occurred in the twelve-month period ended January 27, 1960. B oth It is noteworthy that the decline in pri vately held demand deposits in the twelve month period ended January 25, 1961, amounted to only 5 percent. By way of con trast, in the twelve-month period ended Jan uary 29, 1958, a period which also included a turnaround in business activity, such deposits declined by more than 7 percent. Moreover, in the 1957-58 period, all types of holders of demand deposits accounts shared in the de cline, whereas in the most recent period only deposits held by business firms were reduced. The number of accounts held by individu als, partnerships, and corporations increased slightly during the most recent twelve-month period. As of January 25, 1961, the estimated number of such accounts totaled 4,372,000, which represented an increase of 24,000 ac counts from the previous year. Table 1 shows (i) Based on the Survey of Ownership of Demand Deposits of Individuals, Partnerships, and Corporations as of Janu ary 25, 1961. This was the fifth annual survey of the same sample of insured commercial banking offices, except for minor adjustments for changes in the banking structure. 14 1958 1959 1960 1961 Note: Figures are plotted for each year as of the last Wed nesday of January. The “ other” category includes ac counts held by unincorporated farmers, nonprofit or ganizations, foreign individuals and firms, and trust funds of banks. A decline in business deposits accounted for all of the reduction in the total of privately held dem and deposits during the tw elve-m onth period ended on the last W ednesday of January 1961. Table 1 DEMAND DEPOSITS OF INDIVIDUALS, PARTNERSHIPS, AND CORPORATIONS BY TYPE OF HOLDER (Estimates for Insured Commercial Banks, Fourth Federal Reserve District) January 29, 1958 TYPE OF HOLDER January 28, 1959 January 27, 1960 January 25, 1961 Number Amount Number Amount Number Amount Number Amount (thou(millions (thou(millions (thou(millions (thou(millions sands) of dollars) sands) of dollars) sands) of dollars) sands) of dollars) Business........................ 403 $5,004 409 $5,064 440 $5,242 443 $4,788 Nonfinancial.............. Financial.................... 385 18 4,379 625 387 22 4,351 713 414 26 4,492 750 414 29 4,150 638 Corporate...................... Noncorporate................ 135 268 4,164 840 137 272 4,087 977 162 278 4,130 1,112 157 286 3,751 1,037 Personal........................ Farmers, Noncorporate All O thers..................... 3,124 160 238 2,396 171 604 3,220 152 249 2,582 170 673 3,514 140 254 2,600 149 685 3,536 133 260 2,601 155 685 T O T A L ......................... 3,925 $8,175 4,030 $8,489 4,348 $8,676 4,372 $8,229 Table 2 DEMAND DEPOSITS OF INDIVIDUALS, PARTNERSHIPS, AND CORPORATIONS PERCENTAGE DISTRIBUTION BY TYPE OF HOLDER January 29, 1958 January 28, 1959 January 27, 1960 January 25, 1961 TYPE OF HOLDER Business................................. Number Amount Number Amount Number Amount Number Amount 10.2% 61.2% 10.2% 59.7% 10.1% 60.4% 10.1% 58.2% Nonfinancial...................... Financial............................ 9.8 0.4 53.5 7.7 9.6 0.5 51.3 8.4 9.5 0.6 51.8 8.6 9.5 0.7 50.4 7.7 Corporate.............................. Noncorporate........................ 3.4 6.8 50.9 10.3 3.4 6.8 48.2 11.5 3.7 6.4 47.6 12.8 3.7 6.5 45.6 12.6 Personal................................ Farmers, N oncorporate.. . . All O thers............................. 79.6 4.1 6.1 29.3 2.1 7.4 79.9 3.8 6.1 30.4 2.0 8.0 80.8 3.2 5.9 30.0 1.7 7.9 80.9 3.0 6.0 31.6 1.9 8.3 T O T A L ................................. 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 15 Business Accounts The decline in demand deposits held by business firms accounted for virtually all of the reduction in the total of privately held demand deposits for the twelve-month period ended on January 25, 1961. At $4.8 billion on the latter date, the volume of business de posits was nearly 9 percent below the yearago level, but only 4 percent below the figure on January 29, 1958. Despite a sharp drop in the most recent twelve-month period, business deposits con tinue to account for the largest single share of the total volume of privately held demand deposits. On the survey date in 1961, such deposits amounted to 58 percent of the total; in 1960, the comparable figure was 60 per cent, while in 1958 it was 61 percent. A breakdown of business accounts by type of business shows that the demand deposits of nonfinancial enterprises, which include mainly manufacturing and trade firms, de clined by a smaller percentage in the twelve months preceding January 25, 1961, than did the deposits of financial businesses. However, the same development can not be found for a longer time span. Thus, when compared with other types of depositors, the relative position of financial businesses was about the same in 1961 as in 1958, while the relative position of nonfinancial businesses declined to 50 percent of the total in 1961 from 54 per cent in 1958. (These relationships are shown in Table 2.) Still another breakdown of business ac counts reveals that demand deposits held by corporations were reduced relatively more than those of noncorporate firms. Demand deposits held by corporations have been in a downtrend in recent years. This development is revealed in both the shrinking volume (see Table 1) and in the declining relative share (Table 2) of the total of demand deposits held by corporations. It has been suggested by a number of observers that much of this development is due to the disposition of corporate money managers to hold working 16 balances, i.e., demand deposits, at a minimum level, and, at the same time, to put tem porarily excess balances to work by obtaining earning assets. Personal Accounts Personal accounts held by individuals rep resented nearly 81 percent, or 3.5 million, of the total number of privately held demand deposit accounts on January 25, 1961. Indi vidual accounts have tended to grow steadily in recent years, both in the number and in the volume of deposits. Over the latest twelve month period, however, the volume of demand deposits held by individuals remained prac tically unchanged while the number of such accounts continued to increase. (It should be noted that over the same period, the volume of savings deposits of individuals at such in stitutions increased markedly.) While the number of personal accounts was in excess of those of all other holders com bined, the former represented less than 32 percent of the total deposit volume. However, personal demand deposit balances accounted for a larger share of the total volume of de posits in January 1961 than in any other recent year, a gain which was made chiefly at the expense of declining business deposits. The number of demand deposit accounts of unincorporated farmers continued to decline between the 1960 and 1961 survey dates, al though the volume of deposits in such ac counts advanced 4 percent. The year-to-year rise in volume was the first increase reported since the survey date in January 1957. De mand deposits held by unincorporated farm ers was the only type of account that in creased in dollar volume during the survey year ended January 25, 1961. The deposit volume of all other ownership groups either declined, as in the case of deposits of business holders, or remained unchanged, as in the case of personal accounts and accounts of ‘ ‘ all other” holders. (The category of “ all other” holders includes deposits of nonprofit organi zations, trust funds of banks and deposits of foreigners.)
@FedFRASER