The Capital Expenditure Function

The Capital Expenditure Function* IKTRODUCTION

The aim of the research project reported in this paper was to formulate and test a theory of investment by firms. Since its object was to investigate the behaviour of firms within the institutional framework of the British economy, rather than to describe the conditions in which they ought to invest, the project is to be regarded as an exercise in positive economic theory.

Central to a properly conceived theory of the capital expenditure function, it is thought, is a correct description of the factors which underlie both the demand for additional capital equipment and the availability of funds for investment a t the level of the firm. While the formulation of the theory in terms of demand and supply functions seems simple and obvious within the context of traditional economic theorising, it appears that the ambiguous role of profits in the investment decision, has, in previous work in the field, obscured the fact that capital expenditure can be seen as a resultant of the two fundamental economic forces.

THE DEMAND FUNCTION The demand for capital equipment is a derived demand ;

it is, in fact, a function of the rate of change of sales of the goods which the capital equipment itself produces. In other words the operation of the acceleration principle lies behind the demand for new real capital, and the simplest specification which corresponds to such a hypothesis is a behavioural equation in which investment is a linear function of changes in saIes :

where Iit = b,dStt (1)

Irt is the investment of the ith firm in period t dStt is the change in sales of the ith firm from period t-1

to period t , and b, is a coefficient.

Such a specification, however, is too simple. In line with arguments previously presented, the demand function has to be

*The author wishes to express his appreciation of the comments of the editor of the Manchester School and his referee : they must, of course, be absolved from responsibility for remaining omissions and com- missions.

133

134 The Maitchester School

modified to take into account the fact that firms do not readily dispose of assets when sales fall, and also that decision and gestation lags occur in the investment decision.

Before we consider appropriate modifications of the hypothesis, it is necessary to comment upon the observable fact that firms do sell off capital assets. The position which will be taken up here is that firms do not sell equipment in response to declining demand in the short term, and that, consequently, the need to modify the linearity of the acceleration principle is unaffected by the possibility of asset disposal. There are two main arguments in support of this position. First of all, it may be maintained that the sale of assets is determined more by the policy of the firm with regard to the replacement of capital equipment than by changing demand conditions. Secondly, even if it is accepted that firms do dispose of assets when sales contract, it is reasonable to suppose that they will only do so after considerable delay. To put it another way, the lags involved in the assets-disposal decision make it improbable that such a possibility is an important factor in a theory of the short-term determinants of investment.

Perhaps the simplest method of adapting the model to take into account the asymmetric response of firms to sales changes is to define a new variable to replace A&.

Accordingly, we define a new variable A*&, where A*SU = Stt-ma. (S t , t-l ; St , t-2 ; Sr, t-g ; St, t-*)

if Stt > max. St , t - , ; St, t-2 ; St, t -3 ; St,t-J = 0 if S < max. St, t-l . . . Si, t-*) (2)

In other words, the demand variable is now defined in such a way that only increases in sales over the previous short-term. maximum are registered positively, and are thus assumed to act as decision variables. The model now becomes :

I t = bl A*& (3) I t is next necessary to consider suitable modifications of

the model so that it can accommodate decision and gestation lags. However, while the arguments for the existence of lags in the decision making process are convincing it would be a mistake to suppose that the firm behaves in a purely mechanical fashion, responding, after a delay, to an increase in sales by a spurt of investment. A more plausible formulation would hold

The Capital Expenditure Function 135

that a non-transient increase in sales would have an immediate impact on current investment, but that a substantial residual influence would remain ungestated until subsequent periods.

The crucial question is the number of subsequent periods which is likely to be affected. Common sense suggests again that no simple mechanical theory is appropriate. In order to adapt to a complex and dynamic environment, a firm must constantly reappraise its policies in the light of currently available information. I t is evident, however, that the number of acceleration variables which affect current investment is a matter for empirical investigation. A complication is that there is the possibility of a feedback mechanism in the decision process.

To understand this, we need only compare the probable reaction of a firm whose sales have increased in two consecutive periods with those of a firm whose sales have increased in the first period but have fallen in the second. While the influence of the first increase in sales may be expended over several subsequent periods in the former firm, in the latter firm it is likely to be modified before its full impetus is used up.

Although the existence of such a negative feedback loop in the investment decision adds a dimension of complexity to the model, the hypothesis which will be tested initially is simple. On the average, it is maintained, an increase in sales, as already defined, has a linear effect on current investment and also on investment in the subsequent period, its influence on later periods being negatived by the feedback mechanism.

The simplifying assumption of course, lies in the fact that no distinction is made between firms which experience two successive increases in sales and firms which experience first a rise, then a decline, in total sales. The model then becomes :

I f t = b,d*Si,t+b,d*Si, t-1 (4 THE SUPPLY FUNCTION

An essential element in a correctly specified model of the investment decision is a description of the financial circumstances in which funds will be available for needed investment. Tliere are two points which are worthy of immediate comment. Firstly, pre\ ious work by Barna' and Meyer and Kuh2 suggests that a

136 The Manchester School

suitable hypothesis will be couched in terms of liquidity flows rather than liquidity stock, as liquidity stock variables have consistently shown no correlation with investment or growth. Secondly, most investigations have sought to find positive relationships between liquidity flow variables and investment thus attempting to define the circumstances in which a high liquidity flow would lead to investment. A typical finding of such investigation is the conclusion put forward by Meyer and Kuh that liquidity considerations are of paramount importance in cyclical downswings.

I t may be questioned whether such an approach is based upon an acceptable premise as to the nature of underlying motives. The hypothesis which will be put forward here is that a high liquidity flow per se provides no incentive to invest, but that a thin liquidity flow can act as a restraint on investment.

In order to ascertain the conditions in which' a firm will experience a liquidity shortage, it is necessary to examine the total liquidity flow position of the firm. In particular it is necessary to take into account the availability of both internal and external funds. A convenient starting-point is provided by Duesenberry's cost of funds schedule.3 Duesenberry's view was that the cost-of-funds schedule is composed of three parts: a comparatively flat section, a gradually rising segment, and finally a section which rises steeply and then flattens out somewhat. These three segments correspond to internal liquidity flows, whose opportunity cost is the expected rate of return from investing in the equity of other firms, external long and medium term loans, and new equity respectively.

The Capital Expenditure Ftmction 137

Duesenberry’s analysis conforms to experience, and accom- modates the well-known preference of firms for internal finance. R. F. Hender~on,~ moreover, estimated that, for share issues of less than fI200,000, the cost of issue lay between 74% and 1576 of the sum raised, a figure which lifts the cost of new equity well above the opportunity costs of internal finance.

If we now make the reasonable assumption that all firms are equally affected at a point in time by the costs of external finance, it follows that the firms which find difficulty in financing investment are the firms which have meagre internal resources. Moreover, these are the firms which are also most likely, for a variety of obvious reasons, to have most difficulty with external financing as well.

Before the simple proposition that firms with a weak flow of internal liquidity are those which encounter liquidity restraints can be accepted, it is necessary to examine the possibility that a firm can expand the flow of internal funds for investment purposes by squeezing dividends. In other words, it is important to consider the flow of funds in relation to the range of obligations confronting the firm. In this respect there is no reason for rejecting the findings of Lir~tner ,~ who has produced an empirically well-founded theory of dividends and by implication, corporate income retention. Lintner demonstrated that the dividend policy of the firm could be explained satisfactorily by the following equation :

where AD = c(D*-D~-J+u (5)

D* = the desired dividend, c = a reaction coefficient, and

ADt = Dt+,-Dt In turn, the desired dividend was related to profits by the equation :

D* = rPt (6) The important feature of the Lintner prescription is the

fact that the dividend pay-out and consequently, company savings, are fixed by the level of profits and a predetermined policy which is represented, for the individual firm, by the values of 7 and c in the equation system. While the detailed reasoning underlying the Lintner specification need not be considered here, it is worth pointing out that a firm which


reduces its dividends is not only likely to have difficulty with even short-term external financing, but also to find its share prices fall. One need not spell out the dangers facing a firm with equity which is undervalued in relation to its assets to make it clear that there are pressures which force firms to conform to the Lintner system.

The argument may be summed up by saying that the flow of liquidity available for investment depends upon the relationship between net earnings and the firm's dividend obligations which are relatively invariant in the face of changing liquidity needs. The flow of internal funds may, indeed, be measured by the familiar earnings to dividends ratio EfD. However, a liquidity supply function based upon the earnings to dividends ratio would not conform to the hypothesis that liquidity considerations are only operative as restraints on the investment decision. What is needed is a method which will test the hypothesis that investment will be cut back when the value of EfD falls below a critical level but will be unaffected by higher values. In fact, the theoretical difficulty may easily be transformed into practical advantage. If we can assume that the critical value of EfD is 1.5 (which is the mean value less one standard deviation for the samples), then we can define a dummy variable L which fulfils the necessary conditions :

L = 1, if EfD < 1.5 = 0, if E/D > 1.5.

The windfall which accrues from the use of this method is that the need for a separate supply function is dispensed with. The new variable L may be added on to the demand function without loss, so that the new equation becomes :

Itt = b,d*SI, t+b,d*St, t-1+b,Lo, t (7)

THE REPLACEMENT PROBLEM A complication in investment models is that firms not only

add to capital stock ; they replace it continuously over time. A model which did not explicitly recognise the importance of capital renewal would suffer from specification error.

A difficulty is that the concept of replacement investment does not stand up to close examination. Although firms do, on occasion, undoubtedly replace plant and equipment by similar

The Ca$ital Expenditure Function 139

plant and equipment, as often as not they will replace written- off equipment with new, improved equipment with greater, or different, capabilities. Indeed, the concept of replacement investment is of doubtful relevance to a dynamic economy in which the aims, methods, and products of the firm evolve continuously over time.

A second difficulty arises from the fact that the variable which is the principal candidate as a measure of replacement expenditure, depreciation expense, is open to a number of interpretations. On the one hand, for example, Meyer and Kuhs took depreciation expense as an additional source of liquidity flow : on the other hand, it might be accepted, following Eisner,' as a measure of inter-film variance with regard to capital consumption.

Both interpretations receive partial confirmation from the normal accounting practices of the firm. While depreciation forms a legitimate part of total expenses in the calculation of net profit, it is not general practice to ear-mark such funds, so that, in general, depreciation expense swells the flow of internal finance. On the other hand, the variation of the level of depreciation expense from firm to firm suggests that it is some- how related to the durability of capital equipment.

It seems, then, that the depreciation variable represents an amalgam of financial and capital consumption influences. Actually, it may be legitimately argued that liquidity considerations predominate in time-series analyses, and that capital consumption provides the key to a correct interpretation in cross-sectional models. Since the policy of the firm with regard to the writing-off of capital is unlikely to vary sharply in the short term, it is improbable that variations in such policies could explain observed relationships between depreciation expense and investment in a time-series study, which is concerned with the experience of a single firm, or group of firms, over time. If depreciation expense is related to investment, then, it is by virtue of the fact that i t is a component of liquidity flow.

In cross-sectional, time-invariant , analyses, however, a different picture emerges. While the liquidity flow aspect of depreciation expense does not disappear, an important additional


influence on the level of depreciation expense is the depreciation policy pursued by the firm. Firms which prefer to replace equipment frequently will, other things remaining equal, have a higher rate of depreciation than more conservative firms. Furthermore, the greater the heterogeneity of the firms in the sample, the more will differences in the level of depreciation expense reflect differences in the rate of capital consumption of firms of comparable size. A sample which included firms from such diverse industries as brewing and heavy engineering, for example, would have annual depreciation rates which varied from 1.5% to 8% of gross fixed assets. I t is clear that in a sample which is not stratified by industries, the level of depreciation expense, suitably transformed to a rate by being expressed as a proportion of gross fixed assets, largely reflects the company’s policy with regard to capital replacement.

Moreover, the present tax regulations with regard to depreciation expense tend to reinforce this interpretation. Though firms obviously vary in their treatment of depreciation the rules applied by the Inland Revenue ensure that tax relief is only given on depreciation expense which is related to a standardised rate of depreciation for different types of equipment. If actual depreciation by the firm conforms broadly to fiscal requirements, as seems reasonable, then the rate of depreciation will be a reasonable measure of inter-firm differences with regard to capital consumption.

Whde it is clear that the rate of depreciation would not influence investment measured as the change in gross fixed assets in a purely static theory of replacement, there will be a relationship if the price of the new assets is higher than the price of the replaced assets because of inflation or because the new assets incorporate, a t a higher price, technical improvements in the industry. In other words the rate of depreciation variable can be expected to absorb in part the impact of both price changes and process innovations on the investment process. If we define the depreciation expense and the gross fixed assets of the zth firm at time t as Rlt and Glt respectively, the new specification is :

I i t = b1 d*Stt + h d*Stt-i+bsR<t/Git+ b,Lit (8)


THE PLACE OF PROFITS I N THE INVESTMENT DECISION The theory as formulated does not hold that the expected

rate of profit is a significant determinant of investment. Such an omission requires comment. There is, initially, a problem of measurement; in the absence of a variable which can accurately represent the expected future rate of profit, the current level of profits has been most frequently taken as the purest measure available of expected future profits or, more accurately, of the expected rate of profit. Profits were not included in this study because they did not perform well in the studies by Meyer and Kuh* and E i ~ n e r . ~ Both these studies attempted to effect a comparison between profits hypotheses and acceleration hypotheses, but they reached different conclusions. Meyer and Kuh found that, although acceIeration influences predominated in periods of expansion, there was some evidence of a relationship between profits and investment in periods of recession. Eisner, on the other hand, found that while simple correlation coefficients between investment and profits were significant, the inclusion of sales-change variables in the model reduced the profits-investment relationship to non-significance, and concluded therefore that profits acted as a proxy for sales.

Meyer and Kuh’s findings about profits have been questioned by Barna, who pointed out that their results were hardly consistent enough to justify their conclusions.l@ In the years when profits ought to have been active in their study, only eight out of a possible thirty individual partial correlations between profits and investment in different industries proved significant : moreover, a close examination of their results reveals that acceleration variables behaved at least as well as profits in the years in question. In such circumstances the possibility cannot be overruled that the partial success of the profits variable in the Meyer and Kuh study was due to their failure to explore fully the influence of lagged acceleration variables.

In this study the hypothesis adopted is that shifts in the firm’s demand schedule rather than a high expected rate of profit provide the motivation for investment. As sales expand, firms will add to capital stock from savings, increasing their equity only when the possibilities of other forms of finance are

142 The Manchcstm School

exhausted. The increased revenue which results will be distributed either by a higher rate of dividend or by a higher total dividend payment which will be paid to the equity which has been increased by bonus issues. In either case the return to the initial equity will be partly in the form of dividend payments and partly in an augmented market value of shareholdings.

THE CAPITAL-OUTPUT RATIO AND THE PRODUCTION FUNCTION In common with other models based upon acceleration

hypotheses, the thesis presented here incorporates assumptions about the production function of the firm. The simplest assumption is that the firm has a constant homogeneous linear production function, and that no changes in input factor proportions take place as capital stock expands. Such an assumption leads to a constant capital-output ratio over time. In reality the picture is rather more confused. Firstly, it is probable that, in many firms, the assumption of constapt input factor proportions is temporarily violated. When sales grow, firms will be forced to resort to overtime working, and it is this change in the capital-labour input ratio which often activates the acceleration process. Secondly, the premise that firms have time-invariant homogenous linear production functions is only approximately true. Some firms will have production functions which yield increasing returns to scale, and others will change marginally their methods of working (production functions) as out put expands.

Fortunately none of these qualifications is likely to damage the assumption of proportionality between capital stock and output in the short run. Changes in the production function, and deviations from homogeneity are likely to be marginal so that unaccounted-for variation in the dependent variable in a regression analysis from this cause will be readily absorbed by the error term. STATISTICAL PROBLEMS

The purpose of this section is to review some of the specific statistical problems which arose during the study. Of the many hazards which beset single-equation models, four merit special comment : these are the problems associated with the need for stratification, heteroscedasticity, varying lags and identification, respectively.


Semple Stratification Although this study has used a sample of firms across

industries, it might be held that it is necessary to stratify the sample by industry group in order to eliminate adventitious variation in the dependent variable which arises solely from differences in industrial structure.

Clearly, there is a measure of truth in the argument. Variations in capital intensity might mean that an increase in sales would cause a different proportional increment to capital stock in one industry than it did in another. Similarly, if the inventory to sales ratio varies from industry to industry, some firms will have to cope with higher liquidity needs than others as sales expand.

However, sample stratification was rejected in this study for a number of reasons. Firstly, apart from the practical difficulties of obtaining a sample of firms from a closely defined industry group, it is doubtful whether the concept of the industry group is nowadays of much relevance. In an age which is characterised by the increasing predominance of multi-plant, multi-product concerns, and in which the most prevalent market structure is monopolistic competition with product differentiation, stratification by industry group provides a somewhat spurious indication of homogeneity, especially when stratification by size is not used as well. Secondly, the theory has been cast in a form which, to some extent, discounts the necessity for classification by industrial origin. The fact that the demand for investment is thought of as arising from the disturbance of an equilibrium or desired capital-output ratio implies that the study is less dependent upon the absolute value of the ratio than upon the relative size of the deviation from it. Indeed such a study has to choose between imprecise industry grouping on the one hand and assumptions about capital intensity which are only approximately true on the other : and it appears that there are few objective grounds for preferring one to the other. Lastly, dispensing with stratification schemes provides a t least one advantage; namely, that it simplifies the investigation of the relationship between rate of capital consumption and investment.

144 The Illatichester School

Heteroscedasticity As is well known, substantial size differences in a cross-

section of firms are likely to conflict with the assumption of the Gauss-Markov theorem on least-squares, that the error variance should be constant from observation to observation. Actually, the effect of such heteroscedasticity is to‘ inflate the calculated error-variance, and hence to lead to inconveniently high standard errors : it is thus prudent in an investigation which depends crucially upon the significance of regression slopes, to attempt to remove or reduce heteroscedasticity.

A number of possible methods exists. Prais and Aitchisonl’ have developed an iterative procedure, based upon a transformation of the variance-covariance matrix of the error terms, which effectively deals with heteroscedasticity. Moreover as G. Fisher has shown, under simple assumptions about the distribution of the error term, the method yields estimators which have the desirable properties associated with the method of maximum likelihood.la Unfortunately, the method is, at least relatively speaking, computationally complex.

A second procedure is to deflate the variables by the use of a suitable deflator, such as gross fixed assets. Meyer and Kuh demonstrated that provided the deflated variables were homogeneous linear functions of the deflator (i.e. that the regression of the deflated variable on the deflating variable passed through the origin), the least-squares analysis wouM yield estimators similar to those obtained by an analysis of the undeflated ~ariab1es.l~ However, it is improbable that the homogenity postulate would be fulfilled in the absence of industry strati- fications. For example, if gross fixed assets were used as a deflator, it would be unrealistic to suppose that the sales-to- gross-fixed-assets ratio was constant from industry to industry as the assumption of homogeneous linearity implies.

The method which was adapted in this study, however, does not depend upon the relationship between the numerator and the denominator of a ratio. Each variable was, where necessary, redefined in ratio form, so that each ratio variable had a clear economic significance. Thus the sales change variables

The Cajital Exfenditwe Function 145

and A*St’ - ‘-I, while the capital stock A*& were defined as - Sr, t-1 St. t-2

I t t

Gt, t-1 variables became - where Ga, t - , denotes the gross fixed

assets of the ith firm at time (t-1). No changes were required in either the “replacement” or “liquidity restraint” variables, which were in suitable form.

Corresponding, of course, to the changes in variables is a change in emphasis of the hypothesis. The new hypothesis is not concerned with the absolute level of investment, and attempts principally to relate the rate of change in capital stock to the rate of change of sales. The advantage of the method is that it considerably reduces heteroscedasticity without introducing assumptions about the ratios. The model is now :

The Problem of Varying Lags The model is based upon the assumption that acceleration

lags are constant from time-period to time-period and from firm to firm. This assumption is almost certainly false. Indeed, when we consider the factors which influence the size of lags more closely, varying lags seem inevitable rather than merely plausible. Thus it is reasonable to suppose that the length of a decision lag will depend upon the extent of pressure on the present capacity of the firm, the availability of skilled labour, the current organisational efficiency of the firm, and a range of other factors, such as the general climate of business expectations, which are external to the firm. In the same way, gestation lags can be expected to vary with the experience of the capital goods industries which supply the additional capacity. In particular, common sense suggests that acceleration lags conform to a cyclical behaviour pattern, and that, in the upswing, their lengths will vary with the amplitude of the cyclical fluctuations.

But varying lags can influence the investment process in another way. The model as elaborated up to this point assumes that investment passively follows real increases in sales. If, however, firms invest in anticipation of future increases in sales, there will be a negative acceleration lag in the model.

1 o *

146 The Munchester School

More generally it is reasonable to assume that = Ij ; ) + r p (10)

where I!;) is due mainly to acceleration pressure which has not been previously anticipated and to “replacement” investment : and where Iif) is investment which anticipates future increases

in sales. If we now assume that - is to be explained by rj;) Gi, t-1

It;’ equation (9), while - is explicable in terms of a linear

Gt, t-1

theory of expectations : 1% - A*&, t A*St, t-1

+ CaSZ,b-2 -- Gt, t-1 St, 1-1

we get, by adding (9) and ( l l ) , I:” 1 ‘2 ’ +- Gt, t-1 Gi, 1-1 Gt. 1-1

--- - Itt

Since (12) is identical in form with (9), it is clear that the model can encompass “expectational” investment as well as “induced” investment. The price which has to be paid, however, is that the problem of varying lags is likely to be exacerbated, since the extent to which one firm anticipates increasing sales is likely to differ from the extent to which other firms anticipate increases in sales. This variation in lag structure has potentially serious implications for regression studies predicated upon the hypothesis of fixed lags. It is evident that the variation in lag structure from firm to firm will have the effect of depressing the regression coefficients and inflating the error variance.

Identi$cation Identification problems arise in the estimation of the model

because of the correlation between profits and sales. The net result is that a specification which contains either profits or sales may give rise to conflicting interpretations, depending on whether profits are regarded as a proxy for sales or vice-versa. Although discussion of the identification problem will be deferred until later, the existence of a high correlation between profits and sales allows us to circumvent one serious practical difficulty ;

The Capital Expenditure FutictiotL 147

the non-availability of sales figures in the U.K. If we replace sales by trading profits, we can derive estimators which at least have the desirable asymptotic property of consistency. * Denoting trading profits by P , there results the specification :

Finally, in order to express the model in a form suitable for statistical estimation, it is necessary to add a constant term and a disturbance U, so that the final form is :

THE SAMPLE Estimation of the model necessitated data from a cross-

section of accounts of manufacturing companies. The data for the study was obtained from Exchange Telegraph cards which contain, in summary form, information from the financial statements of public companies.

The original intention was to utilise data from a sample of about one hundred medium and large-sized firms for two successive years, 1963 and 1964, so that the hypotheses could be tested on the same firms for two consecutive time-periods. Unfortunately this proved impossible for a number of reasons. Firstly, a large number of firms had to be eliminated because they had experienced a pattern of falling sales over the previous years. Since the hypotheses to be tested held that the main impulse to invest came from expanding sales, such firms were clearly unsuitable. Indeed a cursory examination of these firms lent a certain prima facie credence to acceleration reasoning, since the typical reaction of the firm to falling sales was dis- investment, as evidenced by a pattern of declining net fixed assets.

Secondly, a considerable number of firms had to be removed from the sample because of mergers within the period of the study. Mergers and acquisitions of subsidiaries were an

*Meyer and Kuh found that replacing profits figures by sales figures yielded very similar results. The use of trading profits as a proxy for sales in a cross-section model gives rise to the additional difficulty that the same percentage increase in profits may represent different percentage changes in sales in different industries.


extraneous cause of asset growth, and since it is impossible to disentangle changes in assets due to this cause and changes due to investment, it was necessary to reduce the sample by these firms.

Thirdly, for most firms, it was found impossible to obtain figures of investment for two years, so that the final sample was divided into two parts : a sample of 29 firms with 1963 data and a sample of 30 firms with 1964 data.* The reason for this was the definition of investment chosen, the percentage change in gross fixed assets over the previous year, required Exchange Telegraph cards for two consecutive years for each firm, since Exchange Telegraph cards in general contain only the value of gross fixed assets for the current years ; and it proved impossible to obtain cards for more than two consecutive years. The alternative definition of investment, the percentage change in net assets, would have permitted data to be obtained more easily, but with such a definition, investment figures would be affected by fluctuations in inventory levels, and as such would be misleading. The industrial origins of the 45 firms in the study are shown in Table I.

TABLE I

Chemical and Allied Industries Engineering . . . . . . . . . Electrical Engineering ...

Clothing and Textiles ... Food and Drink . . . . . . Building Materials . . . . . .

Metal Working . . . . . .

... 6

... 14

... 5

... 1

... 9

... 4

... 6

45 - -

SHARE AND DIVIDEND POLICIES Since the model contained a number of general assumptions

about the financial behaviour of finns, a brief survey of the data was made to confirm that none of the pre-conditions were violated.

In the event the assumptions seemed to be reasonably well founded. First of all, the share policies of the firms conformed reasonably to the belief that firms concentrate heavily upon

*'llie exact data may be obtained from the author on request.


internal finance. No firm raised external finance by the issue of new equity during the period of the study. On the other hand all firms in the study had made scrip issues within the previous ten years, and no less than twenty-one made bonus issues in the years 1962-64 ; figures which lend credibility to the view that firms use scrip issues to expand their equity pari passu with their assets and their revenue.

Moreover, the dividend policies pursued by the firms showed at least on superficial examination a general conformity with the Lintner thesis. Lintner's model covers two main categories of firms: those which follow a straight line dividend policy, and those which adjust dividends, perhaps after a delay, when profits change. Among the firms in the study some sixteen had straight line dividend policies. Twenty-one seemed to fall into the second category ; and the remainder had policies which were obscured by frequent scrip issues.

THE RESULTS Using the method of single-equation least-squares, the

coefficients of the model were estimated from the two sets of data, with the following result :

TABLE 11 (1%3) I I

A *Pt-l/Pt-2 . . . . . . 0.45 2.98'

RtlGt . . . . . . . . .) 1.85 I 2-05"

Lt . . . . . . . :::I -12.19 1 -2.445''

- Constant ... -7.7384

R' = 0.550

Mean

10.22

11.75

5-1 3

0.1 38

The lllanchesfer Sch,ool

Variable

A *Pt/Pt-1 . . . . . . A *A-l/Pt-2 . . . . . . Rt/Gt . . . . . . . . . Lt . . . . . . . . . Constant . . . . . .

TABLE 111 (1964)

Regression Coefficient

~1382

3234

1.31

-3.327

-0.573

Regression Coefficient + Standard

Error

2.0SN

2.86’

2.66’

- 1 .#”‘

-

M~~~

15.63

10.86

4-99

e l 67

-

’ Significant at 1% level ” Significant at 5% level ”’ Significant at 20% level

THE DEMAND VARIABLES The initial results provide reasonable confirmation for the

maintained hypothesis. All four of the relevant regression coefficients emerged as strongly significant, some three of them at the 1% level. However, two aspects were intriguing. First of all, the regression coefficients in the 1963 model were significantly higher than in the 1964 data, and the order of magnitude from year “t” to year “1-1” of the coefficients was different in the two years.

To some extent, of course, differences between the two years can be expected from obvious sources. Since the estimation procedure has leaned heavily upon the use of instrumental variables, for instance, finite sample estimators must be presumed to be biassed. Also, the differences are to some extent explicable in terms of inter-sample variance. Nevertheless other explana- tions are equally possible : the operation of the “feedback” mechanism might differ from year to year and from sample to sample ; the specification might be incomplete ; and there is a real possibility of a varying lag-structure.

One method of finding whether there is indeed negative feedback is by testing the model on a reduced set of data obtained by eliminating firms whose sales had not increased nionotonically during the period of the study (in other words,

The Capital Expenditwe Function 151

Variable

by eliminating firms for which a t least one value of A*P was registered as zero), and then comparing with the initial results. The rationale of this procedure is simple : firms which have had fluctuating sales may be presumed to have experienced more powerfully the action of the feedback mechanism ; and the “normal” relationship between investment and the accelerator variables will be perturbed in these firms. It follows that higher values of the regression parameters should be expected from the reduced sets. The results of applying this test are shown in Tables IV and V. The numbers of firms in the reduced sets for 1963 and 1964 were 18 and 17 respectively.

TABLE V (1963)

(Complete sample) (Reduced set) Variable

A *Pt-l/Pt-2 ... 0.45 0.51

Regression Coefficient Regression Coefficient (Complete sample) (Reduced set)

A *Pt/Pt-I . . . . . . A *Pt-l/Pt-2 . . . . . .

0.1 38 0.095

0.234 0.368

The results require careful interpretation. In each case the effect of eliminating firms with fluctuating sales performances was to strengthen the larger acceleration coefficient without significantly changing the smaller.

How far do the results support the contention that there is negative feedback ? First of all, the results strongly suggest that the lag structure varies from firm to firm. In the 1963 results, the first coefficient is significantly greater than the second; and in the 1964 results there is a high degree of probability that the second is greater than the first. A possible interpretation is that the first sample mostly contained firms



which responded to an increase in sales both by a quick adjust- ment of capital stock and possibly by investment in anticipation of further increases, while the 1964 sample was predominantly composed of firms whose reactions were more sluggish. At any rate, the most probable explanation of the varying order of magnitude of the regression parameters from sample to sample is a varying lag structure. If we accept the hypothesis of varying lags, in fact, the change in the coefficients corroborates the existence of the feedback mechanism. The effect of negative feedback can be expected to modify most the strongest influence on curreni capital expenditure, and the data have conformed broadly to this predicted behaviour pattern.

The logical next step was to test whether adding a third

acceleration variable - , added significantly to the explained

variance. Accordingly, the new variable was added to the model, and the coefficients were re-estimated. The results are shown in Tables VII and VIII.

In the 1963 data, the results are rendered confusing by inter-correlations among the determining variables. The new acceleration variable proved significant, but its inclusion had the effect of reducing three of the other variables to non- significance. The main cause of this was a simple correlation of 0.57 between the second and third acceleration variables, and lesser degrees of inter-relationship among the other determining variables.

TABLE VII (1963 Data)

A*Pt-2 Pt-3

I Regression Coefficient f Standard Error Variable

RtlGt . . . . . . . . . Lt . . . . . . . . .

1.538 1.91

-7-539 -1-60

A *Pt/Pt-1 ... ...I 0.511 I 3.36

A *Pt-l/Pt-2 ... ...I 0.165

A *Pt-2/Pt-3 . . . . . . 0.307

0-967

2.80



TABLE Vlll (1964 Data)

Regression Coefficient + Standard Error Variable

A *Pt-l/Pt-2 . . . . . . A *Pt-2/Pt-3 . . . . . . Rt/Gt . . . . . . . . . Lt . . . . . . . . .

0.238

0.067

1 -23

-3.92

A *Pt/Pt-1 . . . . . . 1 2.11

A *Pt/Pt-1 . . . . . . A *Pt-l/Pt-2 . . . . . . A *Pt-2/Pt-3 . . . . . .

0.55

0.31

0 4 2

2.87

0.69

2-42

-1.53

RZ = 0-576

Although, in such circumstances, statistical confirmation for the hypothesis is not available, the results are nevertheless suggestive. There is no a pr imi reason for supposing that two successive increases in profits or sales should be correlated. Indeed, it might be maintained that in a cross-section of firms, both profits and sales would show substantial first-order auto- correlation, and the appropriate transformation to reduce such auto-correlation would be to take first differences. It is therefore not unreasonable to suppose that all the coefficients would have turned out significant but for multi-collinearity. In fact it can be shown that when the independent variables are orthogonal to one another, the partial regression coefficients are identical with the simple regression coefficients obtained by regressing the dependent variable on the independent variables in turn, The simple regression coefficients are given in Table IX.

TABLE IX

Variable I Regression Simple Coefficient


A *Pt/Pt-1 . . a ..a

A *Pt-l/Pt-2 . . . . . . A *Pt-2/Pt-3 . . . . . .

No such difficulties of interpretation arise with the 1964 results. The addition of the third acceleration variable did not add significantly to the explained variance, and the other coefficients were virtudy unaffected.

In order to examine the possibility that the influence of the third acceleration variable was obscured by feedback, the firms with fluctuating sales were eliminated, and the regressions were repeated on the reduced sets which contained seventeen and fourteen firms respectively. The results are shown in Tables X and XI.

TABLE X (1963 Data) I I

0.511 0.955

0465 0.178

0-307 0.247

Regression Coefficient I (Reduced Set) Variable

TABLE XI (1964 Data)

Regression Coefficient omplete Sample) (Reduced Set)

. . . . . . 0.107

. . . . . . 0.505

0.336

A *Pt/Pt-1

A *Pt-ifPt-2

A *Pt-2/Pt-3 . . . . . .

Variable

In the 1963 results, the value of the first regression coefficient was significantly increased, but the problem of multi- collinearity was not eliminated, since there remained a correlation of 0.63 between the second and third acceleration variables. In the 1964 data, however, the coefficients of the second and third acceleration variables were increased substantially. The results suggest therefore that the interaction of lagged effects and the feedback mechanism can explain the initial non-significance of the third accelerator variable in the 1964 data. This conclusion is somewhat weakened by the failure of the coefficient of the

The Capital Eq5enditure Function 155

third acceleration variable to achieve significance, probably due to the loss of degrees of freedom.

THE LIQUIDITY RESTRAINT VARIABLE Even if the arguments upon which it is based are accepted,

there are two obvious criticisms of the liquidity restraint variable which need to be discussed. Firstly, it assumes unrealistically that all firms are faced with similar liquidity needs : secondly, the critical value of E / D chosen, 1.5, is bound to be to some extent arbitary.

It must be admitted that these criticisms are to some extent valid. Internal funds have not only to finance investment and equity dividends, the two demands explicitly considered in the behavioural equation : they have also to finance increased inventories and fixed interest payments to other forms of security. Moreover, accounting conventions are such that net earnings may not refer to a flow of available funds but may reflect changes in stocks and work-in-progress. Since the influence of these factors is likely to vary from firm to firm, it is clear that the earnings to dividends ratio is a somewhat imperfect indicator of the firm’s financial poxition.

Again, the problem of selecting a suitable “critical” value of E / D was not an easy one. It might be thought that firms with less than average values of EID would have difficulty in financing investment initiated by a sudden increase in sales. In this study the figure of 1.5 was chosen because it represented, for the samples, the mean value of E/D less one standard deviation. Four out of twenty-nine firms in the first sample, and five out of thirty in the second, had earnings-to-dividends ratios which fell below this figure, which suggests, not un- reasonably, that most firms operate policies which ensure an adequate flow of funds to meet most contingencies. Although a measure which related the flow of funds available to the funds needed to respond to current acceleration pressure would have been better, it turned out, in the event, that there was a fairly high probability that there was a significant negative relationship between investment and Iow internal liquidity flows, though the relationship is less well founded than the acceleration hypotheses.


CONCLUSIONS This study was based upon the assumption that the capital

expenditure of the firm could be explained in terms of the demand conditions facing the individual firm rather than by reference to the current level of macro-economic equilibrium. Statistically, the hypothesis seems to be reasonably well supported, since the acceleration variables, suitably corrected for asymmetric responses to positive and negative changes in sales, proved strongly significant for both the current and the immediately previous time-period. There was evidence, also, of a negative feedback loop in the investment decision. While common sense predicts that firms will not be responsive to distant changes in demand conditions which do not have contemporary relevance, there were indications that feedback produced a somewhat different effect. Firms which experience a fall in sales will react in a modified manner to subsequent improvements in demand.

An attempt was also made to test whether the inclusion of a third acceleration variable added materially to the explained variance, but the attempt was complicated by multi-collinearity in the first sample, and proved negative in the second. Although no proposition with the status of an empirically verified hypothesis can be put forward, further tests suggested strongly that the initial failure of the third acceleration variable in the 1964 sample was due to the operation of the feedback mechanism. A complicating factor was that there appears to be a varying lag structure from firm to firm and hence from sample to sample which is accentuated by the possibility that some firms had a negative acceleration lag : that is, they invested in anticipation of future sales increases.

Other influences which proved to be important were the rate of depreciation and the liquidity position of the firm. Variations in the rate of capital consumption turned out to be a significant cause of inter-firm variance in investment, accounting for between six and ten per c$nt of the increase in gross fixed assets on the average. In the same way, the results suggest that the minority of firms which have fixed obligations which are high in relation to their current accruals, are in general forced to retrench on investment.

The Capital Expenditure Functioib 157

SOME QUALIFICATIONS The most obvious criticism of the findings is that they are

open to a second interpretation because of the identification problem. A simple examination of the model suggests that significant results can support the contention that firms invest because of a recent history of expanding profits. Actually, apart from the arguments which were mobilised earlier to question the place of profits in the investment decision, there is an important reason for believing that the identification problem does not pose great difficulties in this case. This study has sought to elucidate the causes of investment in a sample of firms which has experienced growth of sales ; in other words, it was concerned with circumstances in which Eisner and Meyer and Kuh found acceleration hypothesis superior to profits and liquidity flow formulations. The aim of the project was not to mediate between profits and acceleration theories, but to explore the dynamics and limitations of a particular acceleration hypothesis in an investment situation which previous work had shown to be explicable in terms of some form of acceleration reasoning. To put the point in -a different way, a study of previous work in the field led to the conviction that acceleration pressure was the sole cause of “induced” investment, and it was only logical to test the resulting specification where, by hypothesis, it was applicable.

A more serious limitation, perhaps, is that the model takes no account of “autonomous” investment, which has been undertaken to exploit a new invention or to manufacture a new product. Unfortunately there is no method available either for separating induced from autonomous investment or for pre- dicting autonomous investment ; and to the extent that firms in the study undertook such investment, the model suffers from specification error.

University of Strathclyde, Glasgow. ALEXANDER B. JACK.

1 1


REFERENCES

1. “Investment and Growth Policies in British Industrial Firms”, Occasional Paper No. 20, N.I.E.S.R., 1962. T. Barna.

2. “The Investment Decision”, J. Meyer and E. Kuh, 1957.

3. “Business Cycles and Economic Growth”, J. Duesenberry, 1958.

4. “The New Issue Market”, R. F. Henderson, 1951.

5. “Distribution of Incomes of Corporations among Dividends, Retained Earnings and Taxes”, J. Lintner, Proceedings of the American Economic Review, 1956.

6. Op. cit.

7. “A Distributed Lag Investment Function”, R. Eisner, Economelvica, 1960.

8. Op. cit.

9. op. cit.

10. Review of “The Investment Decision” by J. hfeyer and E. Kuh, Economic Journal, June 1957. T. Barna.

11. “The Grouping of Observations in Regression Analysis”, S. Prais and J. Aitchison, Review Int. Stat. Inst., 1954.

12. “Maximum Likelihood Estimators with Heteroscedastic Errors”, G. R. Fisher, Review Znt. Stat. Inst., 1957.

13. “Correlation and Regression Estimates when the Data are Ratios”, J. Meyer and E. Kuh, Econometrica, 1955.

The Capital Expenditure Function

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