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Tobin's q and Industrial Organization


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Tobin's q and Industrial Organization by Lindenberg and Ross (1981)

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Tobin's q and Industrial Organization

  1. 1. Tobin's q Ratio and Industrial Organization Author(s): Eric B. Lindenberg and Stephen A. Ross Reviewed work(s): Source: The Journal of Business, Vol. 54, No. 1 (Jan., 1981), pp. 1-32 Published by: The University of Chicago Press Stable URL: . Accessed: 21/02/2012 17:16 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Business.
  2. 2. Eric B. Lindenberg American Telephone and Telegraph Company Stephen A. Ross Yale University Tobin's q Ratio and Industrial Organization* I. Introduction The use of modern financial economics and of financial data to explore issues in industrial organization is just beginning. Financial price data provide a viewing window into the firm through the market's valuation of the securities issued by the firm and the changes in these values over time. Accounting data, on the other hand, provide information on the resources used by the firms. Thus, comparing accounting data and financial valuation data offers the opportunity to examine performance, the difference between inputs, on one hand, and output, on the other. This paper develops such a comparison between accounting data and financial data to examine the extent, distribution, and history of monopoly rents and quasi-rents in the industrial sector.' The basic idea of our approach is to use the difference between the market value of the firm and its replacement cost as a measure of or bound for monopoly rents. The analysis is based on the pioneering insights of Tobin, who introduced the variable q, the ratio of market value to replacement cost, into macroanalysis (see Tobin and Brainard 1968, 1977; and Tobin *We wish to thank an anonymousreferee for his helpful comments. 1. Other papers discussing this subject from somewhat different approachesinclude Thomadakis(1976, 1977) and Sullivan(1977a, 1977b). (Journal qf Business, 1981, vol. 54, no. 1) ? 1981by The University of Chicago 002 1-9398/81/5401-0004$01.50 1 This paperexaminesthe relationshipbetween accountingdata and financialmarketdata to determinethe extent, distribution,and history of monopoly and quasirents in the industrial sector. Our basic idea is to use Tobin's q ratio-the ratio of the marketvalue of a firmto the replacementcost of its assets-as a measure of, or bound for, the monopoly rents of that firm.We develop a data base of q ratios for a sample of firms and relate q both theoretically and empiricallyto other traditionalmeasures of monopoly power.
  3. 3. 2 Journal of Business 1969, 1978). Tobin's intent was to examine a causal relationship between q and investment. He argued that if, at the margin, q exceeded unity, firms would have an incentive to invest, since the value of their new capital investment would exceed its cost. It is clear that if all such investment opportunities were exploited, the marginal value of q should tend toward unity. We will employ this argument peripherally below, but our focus is somewhat different. Our interest is in the cross-sectional value of q and its implications for industrial organization in general, and the measurement of monopoly power in particular. The essence of the argument is that for a competitive firm, one would expect q to be close to one, and as we examine firms with increasing monopoly power (increasing ability to earn above a competitive return), q should increase. If a firm's q is greater than one, the market value of the firm is in excess of its replacement cost. If there is free entry, other firms could enter the industry by purchasing the same capital stock as the existing firm. Furthermore, they would anticipate an increase in value over their investment because its market value would exceed its cost. Thus, in the absence of barriers to entry and exit, q will be driven down to one as new firms enter (or existing firms expand if average and marginal q coincide). Similarly, a firm which is regulated so as to earn no monopoly rents would also have a q close to one.2 A monopolist, however, who can successfully bar entry and is not adequately regulated will earn monopoly rents in excess of the ordinary returns on the employed capital. The market will capitalize these rents, and the market value of the firm will exceed the replacement cost of its capital stock, that is, q will persist above one. But the actual q value of even a competitive firm may differ from unity. There are two principal reasons for this. First, the firm may possess factors of production on which it earns ordinary Ricardian rents, and these may not be captured in its replacement cost figures. To the extent that the firm possesses factors which lower its cost function relative to that of the marginal firm, it will be inframarginal to the industry and will have q in excess of one. Of course, such factors should be capitalized in replacement cost as well as in market value, but this omission, which tends to bias q upward, is avoidable only to the extent that the market value of these factors is carried on the books. For some firms, though, this effect will be mitigated by an opposite tendency. If the firm is not investing in its existing capital stock, for example, if the firm is "dying," perhaps part of a dying industry, or if there have been particular types of technical progress which make its capital stock obsolescent, its q can fall short of unity 2. Leland(1974)has also discussed the relationship betweenreplacement cost andfair rate of returnwithin a regulatoryframework.Of course, if the factors which constitute entry barriersare completely capitalized,replacementcost would rise to marketvalue and q would be unity.
  4. 4. Tobin's q Ratio and Industrial Organization 3 even if it is earning monopoly or Ricardian rents. To put it simply, a firm whose capital stock is simply not worth replacing can have q < 1.3 In general, though, for firms engaged in positive investment, in equilibrium we expect q to exceed one by the capitalized value of the Ricardian and monopoly rents which the firm enjoys. Since the former cannot be negative, the q value of the firm will provide an upper bound to its monopoly rents. This paper will develop the arguments outlined above and compare this new measure of monopoly power with more traditional approaches to the problem. Section II develops the theory in an analytic framework which makes specific the relationship between q and monopoly rents. In Section III, we develop a procedure for constructing a data base of q for a large sample of firms. We also discuss the issues which arise in implementing the theory and, in particular, the sources of the differences between measured q values and equilibrium values. In Section IV, we use this data base to examine empirically several alternative q-based measures, or bounds on monopoly power for the firms in the sample. In Section V, we test the theory by comparing these measures with two traditional approaches to the measurement of monopoly power: the Lerner index and the four-firm concentration ratio. The final section briefly concludes the paper and suggests some further applications of the q measures in industrial organization and policy problems. II. A Theory of q and Monopoly Profits In this section we develop a theory of q which links this variable to the firm's stream of revenues and costs. We begin by specifying the net revenues of the firm, since this is the stream which a competitive securities market will capitalize to obtain the firm's market value, M. If p denotes the price (vector) of the firm's output and Q denotes its output (vector), total revenue is given by pQ. If we let L denote the use of variable factors of production (e.g., labor) and w is the current rental cost of these factors, the firm's net revenue is given by R = pQ -wL. (1) It is this net revenue stream which the securities market values, presumably on the assumption that firms are attempting to maximize this value subject to the constraints under which they operate. Such constraints are of a technological, an economic, and a regulatory nature. The resulting value assigned by the market is the valuation of the fixed factors embedded in the firm, and these include invested capital (and land) and all of the intangible factors on which the firm earns rents. The 3. The reverse is also possible, and a firm which is growing so rapidly that it is outpacingits capital goods supply sources, i.e., its factor marketsare not clearingat existingcapitalgoods pricesanda demandqueueis forming,may haveq > 1 even though it is earningno excess rents.
  5. 5. Journal of Business 4 firm's assets fall into three broad categories. First, there are those which are sold in the market and which make up what is traditionally thought of as the capital stock of the firm. In this category would fall plant and equipment, inventory, and so forth. The second category is composed of those special factors which the firm possesses which lower its costs relative to those of competitive or marginally competitive firms. These factors would presumably be valued for their costreducing abilities. For example, a firm might have special access to a river whose waters are so cold that it can provide industrial coolant more efficiently than that of its competition. The third category of capital is subtler still, and it is made up of those special factors of production which the firm possesses which act as barriers to the entry of competitors. Without being unduly specific about what forms these could take, for example, patents or scale economies, we will identify the net revenues attributable to them as monopoly rents. In sum, then, the total market value can be represented as M = MK + MA + MN, (2) where MK, MA, and MN are the capitalized values of the rents attributable to invested capital or replacement capital K, firm-specific factors A, and, finally, monopoly profits N, respectively. To examine this breakdown in detail, we will have to look closely at the investment behavior of the firm, since this is the prime endogenous determinant of the intertemporal behavior of net revenue R. A firm making additions to its capital stock at time t will do so up to the point at which the marginal value of a further addition is equal to its unit cost ct. For simplicity, we assume that capital depreciates at a true economic exponential rate 8. Technical progress is assumed to be capital augmenting and to occur at a rate 0, and we measure capital in efficiency units, that is, Kt will denote the amount of time 0 capital stock units to which the total capital stock at time t is productively equivalent. With these assumptions, the marginal value of an investment increment at time t is given by its present discounted marginal contribution to the net revenue stream4 0 PVt t e'RK(KT, T)e(8+r)(T t)dr, (3) where r is the firm's discount rate and RK(KT,z) is the marginal net revenue contribution at time i from an increment to investment. The first-order condition which characterizes the optimum level of investment is simply 4. Whilewe are not explicitlytreatingtaxes as an expense in this argument,they can without too much difficulty.Equations(3) and (5) will be modifiedto be incorporated account for the firm's marginaltax bracket, its rate of investmenttax credit, and its depreciationrate for tax purposes. The theory that follows can also be modified to include tax effects, but the essential message remainsthe same.
  6. 6. 5 Organization Tobin'sq Ratioand Industrial (4) ct=PVt, for all t at which investment is positive. Differentiating (4) with respect to time, we obtain the marginal pricing relationship5 et = (0 + r + 8)ct - e'tRK(Kt,t). (5) Notice that this relation is satisfied by firms which are engaged in positive investment, but not, in general, by firms which are not expanding their productive capacity. For such firms 00 Ct > PVt = eotf RK(KT,7)e - (8+r)(T-t)d7. t We will refer to capital goods and firms for which (5) holds with inequality as "dying," and they will be treated separately. Ignoring tax effects, we can use the marginal pricing relation to determine the share of total market value attributable to currently installed capital. In fact, with investment anticipated in the future, the current value of the share of return imputed to capital, net of future investment, is simply the current replacement cost of capital. To see this, we evaluate the return imputed to capital, KRK, minus the cost of new investment, cI, making use of the capital growth equation K = eOt (6) -8K. From (5), the imputed current value of the existing capital stock and of future investment prospects is given by6 cI)e-r(T-t)dr (KRK- - f {r(o 8 + r)c + f {[(O 8 + r)c + [r rce = - c]KeOT - cI}e r(T)dr r f -r OT - = cKe - I OT)e cK - )e -j(cKe cKeOTe_r(T-t)dT rf (cKe c]K - - (cK)e-oTe-r(T-t) 8cK}e-OTer(T-t)dr (7) dr | r(T-t)dr JOt . 5. The dot over a variableindicates a derivativetaken with respect to time. net 6. To ease the notation,we will referto marginal revenueas simplyRK,recognizing that it depends on time and on the level of capital employedat that time.
  7. 7. Journal of Business 6 Since Ke-0t is the number of new units of capital which would be required to replace the existing capital in the firm at time t, this is simply the current replacement cost RCt, where we will define replacement cost as the cost of the most efficient technology which can produce the output flow. (See the Appendix for a further discussion of the influence of technical progress on replacement cost.) The market value of the firm, which is the present worth of all receipts less expenditures, can now be decomposed as Mt= =f (R - cI)e-r(T-t)d cI)e-r(T-t)dr + (KRK- = RCt + (R - f (R - KRK)e-r(T-t)dT (8) KRK)e-r(T-t)dr. From our earlier decomposition, then, MK, the portion of value attributable to the existing capital stock is simply the replacement cost RCt, and the remaining value 00 f (R -KRK)e - r(T-t)dr = MA + MN, t is the sum of the values of ordinary and monopoly rents. Notice that, for a growing firm, market value will never fall below true replacement cost since ordinary and monopoly rents cannot be negative, although they can be zero. Notice, too, that this result does not assume competition in the market for new capital goods. Given the prices of such goods, the result hinges only on the existence of a competitive securities market. (While free entry also supports this result, it is not required.) Of course, for a firm which is not currently investing or will cease investing in the future, we have c > PV, and we can actually have Mt > RCt. Such a firm may well be earning rents but not to a degree sufficient to offset the differential between the present value of the capital stock K * PVt, and RCt. We can now turn to the evaluation of that portion of market value which is net of capital payments, that is, MA + MN. At the margin, capital is chosen so that the reduction in short-run operating costs is equal to the rental rate. Since R denotes revenue net of variable costs, it follows that R - KRKis simply revenue minus long-run costs. Letting AC stand for long-run average costs, from our previous analysis we have RCt + f(R Mt= -KRK)e-r(T-t)dr (9) = RCt + f(P -AC) Qe-r(T-t)dr.
  8. 8. 7 Tobin's q Ratio and Industrial Organization MC D/ AC / P + FOR IMPUTEDCOSTS ENTRYBARRIERS AC (ACTUAL) PRICE MR QUANTITY FIG. 1.-Components of a firm's rent This confirms our intuition that the difference between M and RC is the capitalized difference between revenues and long-run costs. Of course, to the extent that costs are imputed but not actually expensed to owned factors, AC will understate true opportunity costs. The difference measures the true monopoly profits attributable to barriers to entry and the remainder is ordinarily rent. Figure 1 illustrates this breakdown for a firm with upward-sloping costs. In a long-run stationary equilibrium, as M approaches RC, P approaches AC. To put the matter differently, qt-1l+ RC f (P - AC)Qer(Tt)dr, (10) and q - 1 is the capitalized value of both the monopoly and Ricardian rents scaled by replacement cost. In this sense it is an upper bound to the value of monopoly rents earned by the firm. Notice, too, that since P : AC in equilibrium, we must have q ? 1. Proceeding with the analysis, from (10) we have qt= + qt - (P - - cI)e-r(T-t)dT f(R 1 qt which implies that (P AC)Qe-r(T-)dT - AC)Qe-r(r-t)di][f PQe-r(T-t)dT
  9. 9. Journal of Business 8 qt ? [fPQe f -r(T-t)dl (AC)Qe r(T-t)d-] -P7 AC We can summarizethis result in the following proposition, which makes use of Lerner's index of monopoly power, the percentage difference between price and marginalcost (see Scherer[1971],p. 50, for a discussion of the use of Lerner's index in measuring monopoly power). Proposition Let S denote the ratio of averageto marginalcost, that is, the elasticity of the cost function. A firmhas decreasingcosts if S > 1 and increasing costs if S < 1. A firm engaged in positive (gross) investment has a Lerner's index, L=- (P -MC) IP I- ISq, (1 where q is "Tobin's q." Equivalentstatementsof this result are (P AC)/AC S q - 1 and q - (1/S) [1/(1 - L)], and with constant returns to scale (S = 1), we have the simple result that L - 1 - (I lq) and q ? I/(1 - L). The intuitionbehindthe effect of scale, that is, the ratio of averageto marginal cost, on these bounds is straightforward.In the constant returnsto scale case, average and marginalcosts coincide. As we have already seen, q capitalizes the difference between price and average cost, which, in the case of constant returns, equals the difference between price and marginalcost. With scale economies, average cost is declining and marginalcost lies below average cost. As a consecost ratio quence, q will only be an upperbound on the price/marginal if it is augmentedby S, the ratio of averageto marginalcost. Similarly, with increasingcosts (decreasingreturns),the bound can be tightened because marginalcost is greaterthan average cost. Consequently, we might expect that the Lerner index inadequatelymeasures monopoly power because of its omission of the influence of scale on the competitive returnlevel. Over time, the rents attributableto factors not included in replacement costs, that is, A, will fluctuate,grow, or decay dependingon how A depreciates, on technical progress, and on how capital and variable factors substitutefor A. But for a monopolistthere will be a persistent wedge driven between price and average cost and this, in turn, will 7. This last result follows rigorouslyfrom the twin assumptionsof homotheticityin productionand constant elasticity of demand. Notice that these variablesare current, i.e., time t values.
  10. 10. Tobin's q Ratio and Industrial Organization 9 drive a wedge between q and unity. Correctingfor scale effects, a similar gap persists between price and marginalcost. Notice, though, thatfor a perfect competitorwe may still have q > 1, with the excess being the valuation of the ordinaryrents earned on specific factors. A similarresult can hold for a regulatedfirminsofaras Ricardianrents in excess of those included in replacement cost are earned on specific factors. (This is equivalent to an underestimateof replacement cost.) The value of q only provides an upper bound to monopoly power; a firm may have a true index below the bound. Of course, for a firm which is not currentlyinvesting or which foresees significantperiods of no gross additionsto its capital stock, this proposition need not hold. For such a firm, as we have alreadyseen, market value can be less than replacementcost, that is, q < 1. Furthermore, this can hold whether the firm is earning monopoly rents or specific ordinaryrents.8 Finally, we should note that the analysis could be further complicated by explicitly introducinguncertainty and using a competitive valuationoperator(see Ross 1978)to relate the profitstreamto market value, but it can be shown that the basic proposition is reasonably robust to these considerationsas well.9 The rest of the paperis devoted to using the theory of q developed in the analysis above to measure the aggregateRicardianand monopoly rents of a collection of publicly traded firms. The next section will describe the transitionfrom the theory to the data. 8. A modification must also be madefor the firmwith a stock of nonproductive assets, e.g., an excess cash or securitiesposition. Such a stock would addequallyto bothM and RC and tend to bias q towardunity. The extent to which firmshold such nonproductive the assets, though,is somewhatproblematic; line betweenproductiveandnonproductive assets is arbitrary.As a consequence, the effect will be minor, and we will ignore it. 9. To verify this in the simplestfashionassume that randomnet revenuesare distribwith E(5t) uted independently over time as Hlt= H1jt,where 5t is identicallydistributed = 1. From the mean-variance pricingtheory, capital-assetpricingmodel or the arbitrage with no intertemporalchanges in the market price of risk, X, we have the pricing relationship Mt =E(Mt+j E(Iatjl + fItj+) - X cov (Mt+, + I-t+,, market returns) 1 +r + 1 I+r = _ t 1+r (1 - XWl) t + 8HtI 1 +r (+, I 1 T+1I ( A Tt+T (1+ r) where,8 is the covariancebetween5tand the marketreturn.In continuoustimewe would have Mt = ft7(1 - Xf3)HIt+. e r('s-t)ds,which simply scales all of our previousresults by as (1 - X,B) indicated in the text. This constant scaling leaves the basic proposition unchanged.
  11. 11. 10 Journal of Business Table 1 Data Sources Variables TA, HINV, HNP, DEP, I, inventory valuation method, year-end common stock price, shares outstanding, D1, DL GNP deflator-gross private nonresidential fixed investment, wholesale and retail prices indices Preferred stock yield index, bond ratings and yields RNP, RINV Source Expanded Industrial and Utility Tapes (Standard and Poor's COMPUSTAT Services, Inc.) National income and product accounts, U.S. Department of Commerce COMPUSTAT Standard & Poor's, Moody's industrial and utility manuals SEC 10-K reports (computerized file supplied by Standard & Poor's COMPUSTAT Services, Inc.) = total assets as reported,HINV = inventoriesat historicalbook value, HNP = net NOTE.-TA plantat historical book value,DEP = currentbook depreciation expense,I = gross investment (book) in plantand equipment, 1 = total debt maturing 1 year,DL = long termdebts maturing D in beyond 1 cost. year, RNP = net plant at replacementcost, and RINV = inventoriesat replacement III. Proceduresfor Calculatingq Ratios To implement the theory, we will construct a data base of q's for individualfirms. The actual data base descriptions and their sources are given in table 1. In this section we will consider the methods by which q is calculated and why the q measured from this data differs from the actual q of the theory. The calculationof q requires separate calculationsfor marketvalue and replacement cost. Market Value The financialpaper representingownership claims on the firms in our sample are, for the most part, well traded (or have well-tradedsubstitutes), and, in principle,by suitable adjustments,time series of market values can be computed. Insofar as securities markets are as close to perfectly competitive marketsas we can find, the sum of the values of these claims shouldprovide an accuratemeasureof the marketvalue of the firm. The firm's securities fall into three broad groups:'0 (a) common stock, (b) preferredstock, and (c) debt. Throughout,we will assume that recorded year-end common stock market values represent true market values, and these, in turn, fully reflect the informationused in valuing the returns of the firm by equity holders. Because of the difficultyof obtainingcomplete price quotes for preferredstocks, we calculatea firm'saggregatepreferredstock marketvalue by dividingits stock is 10. We are implicitlyassuminghomogeneitywithingroups.Thusall preferred of straightpreferredand all debt is straightdebt. Considerations convertiblesecurities, call provisions, etc., are omitted. Whileeach of these subcategoriescould be pricedout and and dealt with separately,the data requirements availabilitymake the task beyond the scope of this paper.
  12. 12. Tobin's q Ratio and Industrial Organization 11 total preferreddividends by Standard& Poor's preferredstock yield index. (This procedure follows that used by Tobin and Brainard [1977].) This market value of debt is even more difficult to obtain from recorded price data. Much bond trading is done off the floor of the exchanges, so that published exchange data need not fully reflect investors' valuations. One possible way to handlethis is to price out the individualissues using yields associated with the bond ratings of the firm. While this is ideal, the enormity of the task is complicated by the lack of computertapes with the necessary data. As a compromise we have used the following procedure. In any year t, total recorded book debt, Dt, can be broken down as" Dt Dlt +DLt, (12) where D lt is the debt that will mature before year t + 1 (including short-termdebt) and DLt is the long-termdebt maturingbeyond t + 1. We assume that the market value of the debt maturingby time t + 1 equals its book value, Dlt. Long-term debt, however, will have a of marketvalue that depends, significantly,on the maturitydistribution the firm'sbonds, their coupon rates, and the currentyield to maturity. As a first step we estimate the maturitydistributionof each firm'sdebt using the following assumptions:(1) All new debt is issued for n years. (2) In any year, t, the firm moves long-term debt issued in year t - n + 1 into its short-termaccount. It then may retire additionaldebt or add new long term debt. (3) In any year, t, the total long-term debt is the sum of all new debt (N3) issued in the yearsj = t - n + 2, t - n + 1, . . , t - 1, t. (4) Before some initial year, to0 Nj - (1/n) Dto,i = to n + 2, . .. , to. (5) No new debt is issued unless total long-term debt is increased. Under these assumptions it follows that all t > to, . Nt = DLt - DLt-, + Nt-n+l if DLt > DLt-1, (13) and Nt = 0 if DLt - DLt-,. Thus the firm first retires (moves into the short-termaccount) its oldest debt first, then either issues some new debt if net long-termdebt is to be increasedor retires more if desired. It should be recognized that formula(13) may not satisfy exactly the equation Dt j= o Nt-j for all t.'2 Instead of using the values of Nj directly, we obtain the maturity distributionby first estimating the fraction of reportedlong-termdebt, ft,t-j. that was issued new at time t - j as n-2 ttt-i = Nt-j Nt-, = 0, . . , n - 2. (14) k=O 11. Ideally we would like to break the debt down into year-by-yearmaturities,but such data are unavailablein computerizedform. 12. A check was madefor a sampleof 10firmseach of the years 1965, 1970,and 1975. The sum of the estimated new issues deviated from DLt by an average 1%o.
  13. 13. 12 Journal of Business Having established the maturity distributionof the firm's long-term debt, we next proceed to calculate its market value. We employ the followingassumptions:(6) The yield to maturityof a firm'sdebt at time t, when the firm'sbond ratingis Z, is denoted as pz. (7) All new debt at time t, of a firmwith bond ratingZ, is issued at par with a coupon rate equal to pz. (8) The marketvalue, at time t, of a bond is calculatedusing its coupon rate and the currentyield to maturityassociated with that firm's bond rating. With these additionalassumptions, it follows that the marketvalue of a firm's debt (MVDt) can be calculated from D It and DLt by the following formula MVDt = D1t n-2 + DLt Z ft,t-3{(pz jlpI)[I - (1 + pz)-(n-i)] + (1 + p)-(n-i)}. (15) i=0 Summarizing proceduresdescribed above, the firm's total market the value is given by Mt = MVDt + MVt(common stock) + MVt(preferred stock). (16) Replacement Costs The measurementof replacement cost is a more difficult matter because of the lack, in most cases, of active markets for old capital goods.'3 By definition, replacementcost is the dollar outlay needed to purchase the currentproductivecapacity of the firmat minimumcost and with the most modern technologies available (see Appendix). This concept is more complex and more difficultto measure than is reproductioncost, which measuresonly the inflation-adjusted of plantif cost reproducedin kind. To determinereplacementcost we must also adjust for varyinglevels of technologicaladvance across plant categories and producttypes, and for varyingrates of "real" (versus book) depreciation. Nevertheless, the Securities and Exchange Commissionin 1976 began requiringlarge companies to disclose replacement-costdata on their SEC 10-Kfilings(Securitiesand Exchange Commission1976).In particular,replacement-costestimates were requiredin the categories of plant and equipment(gross and net), inventories, depreciationexpense, and cost of goods sold. Unfortunately, for our purposes, the SEC gave broad leeway to firms in the methodology used for the calculations.We use this source to calculate overall replacementcosts 13. For the effect of inflationaccountingon individualfirms, see Davidsonand Weil (1975, 1976)and Falkensteinand Well (1976, 1977).For some work constructingaggregate estimates, see Ciccolo (1975),Tobin and Brainard(1977),von Furstenberg (1977), and Presidentof the United States (1978, 1979).
  14. 14. Tobin's q Ratio and Industrial Organization 13 for the years 1976 and 1977.14 In addition, we construct a series of individual firm replacement costs prior to 1976 using the 1976-77 numbers along with past balance sheet information taken from the COMPUSTAT Expanded Industrial and Utility Tapes supplied by Stan- dard and Poor's COMPUSTAT Services, Inc. The assets of a firm fall into three broad categories: (a) plant and equipment, (b) inventories, and (c) other assets. Category c contains liquid assets such as cash and securities as well as land. Some of these assets are traditionally carried on the books at market value while others are carried at original cost. For our purposes we will assume that the assets in this category have replacement value approximately equal to book value. Categories a and b are the categories for which the SEC has required replacement-cost information. In constructing the time series of replacement costs, we use the following notation: TAt HNPt RNPt HINVt RINVt = = = = = total assets as reported in year t, net plant at its historical value in year t, net plant at replacement cost in year t, inventories at historical value in year t, and inventories at replacement value in year t. Total replacement cost (RCt) is defined as RCt TAt + RNPt - HNPt + RINVt - HINVt (17) for the years of SEC reported data, 1976 and 1977. Prior to 1976, we will consider plant and equipment and inventories separately. The replacement cost of net plant and equipment will change over time as a consequence of four major effects: (1) price level changes (increase RNP), (2) technological change (decrease RNP), (3) real economic depreciation (decrease RNP), and (4) investment in new plant (increase RNP). Given the investment in new plant and equipment series It, the following recursive relation was developed: RNPt = RNPFl[ (1 + t ) + It, t 1, (18) where 0 is the base year (in our case 1952),5 kt is the rate of growth of capital goods prices (for this firm), at is the rate of (real) depreciation, Ot is the rate of cost-reducing technical progress, and the hat above RNP implies that the value is estimated. 14. The accuracyof these dataand the variability the methodsused to constructthe in figuresis discussedat lengthin reportsby the accounting firmsof Arthur Anderson& Co. (1977) and ArthurYoung & Co. (1977). For example, the SEC does not put stringent requirements the reportingof foreign assets at replacementcost. on 15. AlthoughCOMPUSTAT begins its data series in 1946, it is necessary to begin at a later date in order to guaranteecomplete data series for a sufficientlylarge sample of firms.
  15. 15. Journal of Business 14 Continuingthe recursion, we obtain t t - 1+O (1 HS+lL +)s)( RNPt + s) + HNPOH IH (1 (1 )1 + OsOs)'() ) + + + 5s)(l (19) where HNPo is the book value of net plant in year 0.16 Since no satisfactoryand sufficientlycomplete measuresof technicalprogressat the firm level could be found, these were computed endogenously in one of two ways. First, by using the formula(18) for the years 1976and 1977 we obtain = RNP1977 RNP1976 1+ 01i977 + 01977) (1 + 81977)(1 20 I17, (20) If we assume the rate of technicalprogresswas constantfor a sufficient periodpriorto 1976,the solutionfor 01977can be used as an estimatefor t < 1976. The difficultywith this method is that it uses depreciation, inflation, and investment informationfor 1 year only in order to estimate 0 for many years. An alternativeis to calculate0 directlyfrom the formula (19) for each of the years 1976 and 1977 by solving t RNPt ='(I Tr=0 t + ~~~~~~~~~+HP01+0t 11 0)Tt I s=t+Tr + +'I + HNP (1 + 0)-t Ts' H =OI+ I+O (21) 5 (t = 1976, 1977) and then averagingthe two solutions.17These measurementsof technicalprogressat the firmlevel could be aggregatedto the industry level and might be of some independentinterest. To obtainan estimate of the capitalgoods price index, t, we use the GNP deflator for nonresidential fixed investment. The depreciation rate was computed in our study by the formula EHNPt (22) where DEPt is book depreciation. This formula assumes that the real fraction of the (net) assets which depreciatein a given year is equal to the book fraction. This has the virtue of eliminating much of the differencebetween measuredand tax-adjustedreplacementvalues that However, for years of interest 16. To be precise, HNPoshouldbe replacedby RNPO. laterthanthe base year, the differencebetween the real value of the undepresufficiently ciated part of the base year capital and its book value will be negligible. 17. In reality, the value of 0 calculated by this procedure represents not only an effects that estimateof technicalprogressbut includesotherfactors, such as inflationary replacementcosts, and errorsin differfrom the price index, omittedfactors influencing measurementof variables. We refer to 0 as the rate of technical progress in that we believe that this is its majorcomponent.
  16. 16. Tobin's q Ratio and Industrial Organization 15 comes from differences between exponential and straight-linedepreciation schedules. Using these estimates, a time series of RNPt can be constructed for each firm from (18). The other component of replacement cost is the inventory value, RINV. Since different firms use different methods for inventory accounting (e.g., first in, first out [FIFO]; last in, first out [LIFQ], or average cost methods), in principle, different adjustments to book numbersmust be considered for each one. In practice, the differences in FIFO and LIFO methods, for example, have a substantialeffect on the estimated investment series for firms with large inventory positions. In an inflationary period, LIFO will underestimatethe change in inventory value and, as a consequence, the true inventory investment and total actual investment will be understgtedby the difference in book values. The following adjustments Were made for the major methods of inventory valuation reported to Compustatby individual firms.18 LIFO. In this system, units of output sold are assumedto be the most recently purchased units. Consequently, the took value of units of inventory still on the shelf will reflect prices thatunderstatethe cost of replacementin inflationarytimes. Our adjustmen't takes account of the larger undervaluationof old inventory and a smaller underpricingof more recent increments: RINVt = RINVt_ ( I ) Pt-1 + (HINVt - HINVt-1) 5(Pt + Pt-1), Pt-, (23) where Pt is the price index appropriateto inventories. FIFO. In this system, inventories are assumed to be used up in the order in which they were produced. Thus, remaininginventories will be priced on the books at the most recent prices. In fact, if remaining inventories were all producedduringthe most recent period, a reasonable approximationis RINVt = HINVt. (24) Average cost method. In this method, inventory is reportedat time t at roughly an average of the prices at t - 1 and t. Thus our approximation to replacement cost of inventories in this case is 18. Othermethodsinfrequently used by firmsare specificidentification, standard cost methods,andcurrentreplacement costs. In these cases, we used the methoddescribedin the text closest in descriptionto the infrequentlyused method. Also, where several methods were cited for a given firm, the method cited as dominantwas used.
  17. 17. Journal of Business 16 RINVt = HINVt (F2+Pt1 (Pt + Pt-1) (25) (5 Retail cost method. In this method inventoryquantitiesare priced at the expected retail prices. Since producersnormallysell at wholesale, our correction is RINVt = HINVt Wholesale Price Index Retail Price Index (26) (6 we Using equations(23)-(24) where appropriate, can findRINVtfor all can then compute the total replacement-cost years prior to 1976. We series, RCt, by combining RINVt RNPt in equation (17). To avoid any errors introducedby using HNPO,we will discard the beginning periodof the samplefor each firm,from 1952through1959,and confine our analysis to the 1960-77 period. LettingMt denote the estimatedmarketvalue of the firm(from[16]), t we can now construct the series of qit = MitIRC?t, = 1960, ., 1977, where i indexes firms. We have already noted that the idiosyncracies of the accounting conventions make economic interpretationof inventory and investment difficult. The principalproblem with the investment and capital price series, though, is less one of measurementerrorsand more one of the significanceof recordedtransactionsprices generatedin the capital goods market itself. The capital goods industry is highly procyclical, but there is little evidence of this cyclicity in the actual movement of capital goods prices. In an industry with large fixed costs, it is only naturalthat quoted prices will misstate the true costs of acquiringnew capital goods. Cost considerationslead the industry to insulate itself fromthe cycle by producingfor the long run. Thus, explicit and implicit long-runcontracts will be importantcomponents of the capital goods price index. When the demandfor capitalfalls off, actual transactions prices for spot transactionswill decline and longer-termprices will be more sluggish. In periods of high demand, whether the market clears by having demandersqueue at posted prices or whetherthere is a dual system of high spot and lower long-termprices, the effect will againbe to smooth the capital goods price index below the true current spot price. This suggests, of course, that for rapidlygrowingfirms,we might have growth outpacinginvestment and entry. In this case, q would be biased upward, overstatingthe true bound for monopoly power. What we would really like to have is a series of the "gray" or shadow prices rather than the posted transactionsprices. This inherentsluggishnessin the recordedprice index is, of course, reflectedinRC, makingit muchless responsiveto marketforces than is M. Another source of the relative slow variationin RC is the presence
  18. 18. Tobin's q Ratio and Industrial Organization 17 of delivery and order lags. In industrieswith "sticky" capitalwhich is not adjustedto meet currenteconomic effects of the cycle, spot prices will be biased away from the true replacementvalue of the assets. The quoted price may be a spot price, and the relevant currentprice for evaluating replacement cost is not current spot price but a price for forwarddelivery. In this sense, in a period of risingprices, spot prices will understatethe relevantprices for evaluatingreplacementcost. Not only will there be a timingproblem, but the lags imply the presence of real costs to the acquisition of new capital equipmentthat are understated in current capital prices. As a consequence, RC will tend to understate true RC. Furthermore, to the extent to which shifts in demand and supply conditions are accommodatedby changes in the order and delivery lags, prices will respond with a dampenedlag and will move less rapidly than true replacementcosts. The sluggishnessin RC impliesthatqcwill displaya greateramplitude than q. This property underlines much of the hope that qc will have explanatorypower as an independentvariable in determininginvestment. (It is ironic that if qc exactly tracked q-and if there were no distinctionbetween marginalq and averageq-it would lose its value as a determinantof investment.) But, for our purposes, we are interested in trueq itself and not in qc, and we will use qcas an estimateof q. Two other problemsdeserve mention. First, the treatmentof advertising expenditureshas been in accordance with standardaccounting principles, which is to say that we have expensed them. To some extent, though, advertisingis a capital investment and to omit it will bias replacementcosts downwardand q upward.If advertisingcapital depreciatesrapidly,we would expect this effect to be relatively minor. Furthermore,since overall advertisingexpendituresare small relative to replacementcosts, for most firms such a correctionwould be small, and we have chosen to ignore them. Similarqualificationsapply with regard to expensing research and development expenditures. Perhaps a more serious omission is the understatementof firmspecific trainingcosts in investment. Firms which engage in specific trainingmust offer their workers a premiumover jobs which have a higher component of general training. This premium is largely expensed in the wage bill but properly should be added to total investment. Here, too, we tend to bias q's upward. IV. EmpiricalAnalysis The averagesof q, denoted as qi = 1/18Zt=1960 are reportedfor each qit firm in table 2. Our sample selection will be described a bit later. If there are no systematic biases, qi will provide an adequatemeasureof
  19. 19. Journal of Business 18 Table 2 Firms and Average q Values Company ACF Industries AMF, Inc. Abbott Laboratories Akzona Alcan Aluminum, Ltd. Allegheny Ludlum Industries Allied Chemical Corp. Allied Products Allied Stores Allis-Chalmers Corp. Alpha Portland Industries Aluminum Co. of America Amcord, Inc. American Brands, Inc. American Can Co. American Cyanamid Co. American Greetings Corp. American Telephone and Telegraph Ametek, Inc. Anchor Hocking Corp. Anheuser-Busch, Inc. Armstrong Cork Co. Asarco, Inc. Avon Products Bausch and Lomb, Inc. Beatrice Foods Co. Bell & Howell Co. Bethlehem Steel Corp. Borden, Inc. Borg-Warner Corp. Bristol-Myers Co. Brunswick Corp. Bucyrus-Erie Co. Carter Hawley Hale Stores Caterpillar Tractor Co. Ceco Corp. Celanese Corp. Certain-Teed Corp. Champion International Corp. Chicago Pneumatic Tool Co. Chrysler Corp. Cincinnati Milacron Inc. Cities Service Co. Clark Equipment Co. Cleveland-Cliffs Iron Co. Cluett, Peabody & Co. Coca-Cola Co. Colgate-Palmolive Co. Collins & Aikman Corp. Combustion Engineering, Inc. Commonwealth Edison 1960-77 Average q Ratio 1.14 1.43 2.35 1.02 .79 .97 1.26 1.07 1.17 .76 .68 .85 .92 1.23 1.09 1.46 1.94 1.09 1.46 1.17 1.95 1.70 .91 8.53 2.37 1.65 1.64 .68 1.26 .97 3.76 1.23 1.08 1.28 1.52 .84 1.24 .95 1.35 1.13 .90 1.17 1.21 1.51 1.17 1.12 4.21 1.34 1.13 1.14 1.01 Company Cone Mills Corp. Congoleum Corp. Continental Group Continental Oil Co. Cooper Industries, Inc. Copperweld Corp. Corning Glass Works Crane Co. Crown Cork & Seal Co., Inc. Crown Zellerbach Culbro Corp. Cummins Engine Curtiss-Wright Corp. Cutler-Hammer, Inc. Dan River, Inc. Dart Industries Diamond International Corp. Diamond Shamrock Corp. Dome Petroleum, Ltd. Dow Chemical Du Pont (E. I.) De Nemours Duquesne Light Co. Eastern Gas & Fuel Assoc. Eaton Corp. Ethyl Corp. Exxon Corp. FMC Corp. Fairchild Camera & Instrument Federal-Mogul Corp. Federal Paper Board Co. Federated Department Stores, Inc. Ferro Corp Flintkote Co. Foote Mineral Co. Foster Wheeler Corp. GAF Corp. GATX Corp. Gamble-Skogmo Gardner-Denver Co. General Cable Corp. General Electric Co. General Foods Corp. General Motors Corp. General Portland, Inc. General Refractories Co. General Telephone & Electronics Georgia-Pacific Corp. Gillette Co. Goodrich (B. F.) Co. 1960-77 Average q Ratio .45 1.17 1.15 1.69 1.24 .69 3.75 .72 1.41 1.08 1.07 1.35 .95 1.35 .67 1.41 1.50 1.55 2.94 1.62 2.47 .90 1.11 1.17 1.48 1.05 1.47 2.12 1.35 .52 2.06 .97 .86 1.07 .86 1.27 1.10 .97 1.57 1.64 2.07 2.10 1.59 1.09 .70 1.32 1.63 3.92 .89
  20. 20. Tobin's q Ratio and Industrial Organization Table 2 19 (Continued) Company Goodyear Tire & Rubber Co. Grace (W. R.) & Co. Graniteville Co. Great Northern Nekoosa Corp. Grumman Corp. Gulf Oil Corp. Halliburton Hammermill Paper Co. Hercules, Inc. Hershey Foods Corp Holly Sugar Corp. Honeywell, Inc. Ideal Basic Industries, Inc. Imperial Oil, Ltd.-CL A Ingersoll-Rand Co. Inland Steel Co. Insilco Corp. Interco, Inc. Interlake, Inc. International Business Machines Corp. International Paper Co. Iowa-Illinois Gas & Electric Iowa Power & Light Johns-Manville Corp. Johnson & Johnson K Mart Corp. Kaiser Aluminum & Chemical Corp. Kaiser Cement & Gypsum Corp. Kaiser Steel Corp. Kellogg Co. Kimberly-Clark Corp. Koppers Co. Kraft, Inc. Libbey-Owens-Ford Co. Liggett Group Lilly (Eli) & Co. Lone Star Industries Long Island Lighting Lowenstein (M.) & Sons, Inc. Lucky Stores, Inc. Lukens Steel Co. Mallory (P. R.) & Co. Marathon Oil Co. Maremont Corp. Marshall Field & Co. Maytag Co. McGraw-Edison Co. McLouth Steel Corp. 1960-77 Average q Ratio 1.05 1.16 .55 .79 1.06 1.25 1.86 .68 1.86 1.83 .50 2.28 1.08 1.67 1.76 .95 1.39 .98 .75 4.21 1.17 .85 .73 1.24 3.64 1.99 .80 .96 .78 3.20 1.51 .88 1.35 1.47 1.02 4.02 .89 1.28 .61 1.58 .74 1.22 1.81 1.24 1.14 2.71 1.28 .74 Company Mead Corp. Medusa Corp. Melville Corp. Mercantile Stores Co., Inc. Midland-Ross Corp. Minnesota Mining & Manufacturing Co. Mobil Corp. Monsanto Co. Motorola, Inc. NCR Corp. NI Industries Naico Chemical Co. National Distillers & Chemicals National Gypsum Co. National Steel Corp. National Tea Co. Owens-Corning Fiberglass Corp. Owens-Illinois, Inc. PPG Industries, Inc. Pabst Brewing Co. Pennwalt Corp. Pepsico, Inc. Pfizer, Inc. Phelps Dodge Corp. Philip Morris, Inc. Phillips Petroleum Co. Pitney-Bowes, Inc. Polaroid Corp. Potlatch Corp. Public Service- Electric & Gas Publicker Industries, Inc. Pullman, Inc. Quaker State Oil Refining RCA Corp. Revere Copper & Brass, Inc. Reynolds (R. J.) Industries Reynolds Metals Co. Robertshaw Controls Robertson (H. H.) Co. Rohm & Haas Co. Rubbermaid, Inc. SPS Technologies, Inc. Safeway Stores, Inc. St. Joe Minerals Corp. St. Regis Paper Co. Schering-Plough Scott Paper Co. Scovill Manufacturing Co. Searle (G. D.) & Co. 1960-77 Average q Ratio .97 .60 2.21 1.27 1.02 4.87 1.20 1.38 1.97 1.74 1.56 3.69 .94 .92 .53 .97 1.71 1.30 1.05 1.31 1.36 2.31 2.49 1.71 1.45 1.74 1.92 6.42 .82 1.12 .59 .91 1.92 1.67 1.17 1.90 .81 1.11 .89 2.09 2.03 .80 1.14 1.91 .98 4.30 1.46 1.05 5.27
  21. 21. 20 Table 2 Journal of Business (Continued) 1960-77 Average q Ratio Company Sears Roebuck & Co. Shell Oil Co. Signal Cos. Signode Corp. Simmons Co. Singer Co. Smithkline Corp. Southern California Edison Co. Square D Co. Standard Brands, Inc. Standard Oil Co. (California) Standard Oil Co. (Indiana) Standard Oil Co. (Ohio) Stanley Works Sterling Drug Inc. Stewart-Warner Corp. Sun Co. Sunbeam Corp. Sundstrand Corp. Super Value Stores, Inc. TRW, Inc. Texaco, lnc. Textron, Inc. Timken Co. 2.04 1.68 .99 1.69 .90 1.22 4.19 .81 2.68 1.87 1.18 1.24 2.09 .96 3.46 1.20 1.26 1.36 1.17 1.35 1.32 1.86 1.12 1.02 Company Trane Co. Trans Union Corp. UV Industries, Inc. Union Camp Corp. Union Carbide Corp. Union Oil Co. of California Uniroyal, Inc. United Brands U.S. Gypsum Co. U.S. Steel Corp. U.S. Tobacco Co. United Technologies Corp. Wallace-Murray Corp. Warner & Swasey Western Publishing Western Union Corp. Westinghouse Electric Corp. Weyerhaeuser Co. White Motor Corp. Wickes Corp. Wisconsin Public Service Woolworth (F. W.) Co. Wrigley (WM.) Jr. Co. Xerox Corp. Zenith Radio Corp. 1960-77 Average q Ratio 1.82 1.47 1.48 1.43 1.67 1.24 .90 .74 1.22 .62 1.67 .94 .81 1.01 1.33 .83 1.48 1.76 1.12 1.60 .79 .84 1.74 5.52 2.83 true qi and, if we assume thatcqit = atqi and defineqt 1/N it, then is a measure of the relative value of rents earned by firm i. qitlqt However, since our aim is to constructq measureswhich can be used to comparemonopoly and ordinaryrents across firms,to the extent to which there are biases which are common across firms-and the use of a common price index means that most of the biases will be common-we should attempt to correct the raw q values. Several approaches are offered below. The relative variable defined above is one way of dealing with the problems arisingfrom intertemporal changes in q levels. By averaging across firms,we could arguethat individualfirmerrorsshouldwash out in computingqt. The secular variationin qt will measurethe impact of the sluggishresponse of RCt and to assess the impact at the firmlevel, we must remove the variation in qit with the general trend. One approach is to estimate the regression qit = ai + bi(4t - q) + (its where (27)
  22. 22. Tobin's q Ratio and Industrial Organization q 1 21 q Now ai will serve as a measure of the long-run value of qi for the firm.19 An allowance should also be made for the presence of dying firms (firms which are not replacing their capital stock). Since such firms will have their true q below unity, we must correct their q to measure the value of rents earned above their return on invested capital. If we assume that investment at time t occurs in response to differences between PVt and ct, we can use the normalized difference between investment in plant and equipment, on one hand, and depreciation on the other, as a proxy for this difference. Defining 'it min [0, (Iit DEPit)/TAit], one measure of true qi can be found from the regression qit = ai + bi(4t - ') + ci + ( (28) (We also tried (kit - gi) as an alternative.) Here git measures the extent to which firms are not replacing their capacity. Now ai will be a measure of true qi that is corrected for the dying-firm phenomenon. Then, to obtain the corrected value of q at each point in time for firm i, denoted by hit, we have 4it ai + (it, (29) where (it is the calculated residual after performing the regression (28). Alternative formulations to (28), including log-linear forms and the use of weighted averages for q, were also run, but the results described later in this section were not significantly affected. The residual ( is probably best interpreted as describing that portion of firm i's q value that is not explained by economy-wide movements in average q. Of course, to the extent to which the movements in the average q are secular movements in the true underlying q for the economy, this procedure will tend to overcorrect. In particular, in a period of declining q it will remove some of the true decline in a firm's q, and the adjusted trend of q for individual firms will be biased upward from the true trend. Another possible variant of (28) would remove the minimum function in the definition of git so that (28) will also adjust downward the q values for those firms and industries which are experiencing an increase in demand that increases PVt above ct for current investment. the 19. We recognize the fact that in performing regression(27) separatelyfor each firm,the coefficientsof the last regressionwill be functionsof the othercoefficientsdue to the definitionof qt. However, with a sufficientlylarge sampleof firmsthis shouldnot be a significantproblem. We also tried variations of (27), e.g., a log form, but the resultingempiricalanalysiswas not very sensitiveto the specification,andfor simplicity we have not reportedthese results.
  23. 23. 22 Table 3 Journal of Business Adjustment Coefficients for q Definition 1: g Iit- Definition 2: DEPit TAt i =i m ) Iit - DEPit ( TADEPt hi NOTE.-Sample size ei 130 239 201 228 10 15 116 230 7 21 45 2 = hi 236 Positive (N) Significantly > 0 at 5% level (N) Negative (N) Significantly < 0 at 5% level (N) ej 8 2 4 246 firms;N = numberof firmsin each category. As we observe above, the capital goods price index does not measure true acquisition cost in this case, since demanders are queuing for investmentgoods. This may occur even though the firmis not exercising monopoly power. In addition, for firms with heterogeneous mixes of capital goods we cannot conclude that no capital is being replaced simply because depreciationexceeds investment. Of course, the correction is only an approximation both cases, and it is not clear from in the theory alone which form better fits the data. If there is a correlation between growth and true q, we will overcorrect, so that ai will underestimate the true value of qi for high-growthfirms and overestimate it for dying firms. From the sources listed in table 1, data for an initial sample of over 500 firms, for which SEC 10-K informationwas at least in part available, was collected. Firms were eliminatedwhen complete 10-Kinformationin 1976-77 was not available. This left 257 firmsin the sample. When a furthercheck was made for adequate informationfor calculation of Lerner indices in the next section, the sample was reduced to 246 firms.Table 2 lists alphabeticallythe firmsin the samplealong with their respective unadjustedaverage q values. The results of the regressions described above are summarizedin table 3. Using definition 1 (in table 3) for 'it, we find that an overwhelmingpercentageof the bi coefficients had significantpositive signs at the 5%level. This confirmsour intuitionthat bi reflects the responsiveness of measuredqi to economy-wide changes in valuations. We would also expect ci to be positive, but approximately equal number an had positive and negative signs, although these results were insignificantat the 5%level. The results from definition2 of 'it in table 2 were not significantlydifferent, althoughthere was a slight increase in the number of positive ci values. Evidently, the dying-firmeffect is more importantthan the supergrowtheffect, althoughneitherof these
  24. 24. 23 Tobin's q Ratio and Industrial Organization 3.0 2.5 / /TIbi-9j<d / /A 2.0 ~~~~~Lindenberg-Ross' 1.5 - 1.0 Vn-Fu '*@-Fourt I 1960 **.** I I 1961 I 1962 enbeg* I I 1963 1964 1966 I 1966 I I 1967 1969 I 1969 I I 1970 1971 I 1972 I 1973 1974 I I 1 1975 1976 1 1977 Year *-Year E Ad FIG. q 2. -Economy-wide ratios variablesadds much to the adjustmentof q . In fact, we have not listed the values of d, for the firms in the sample since the average adjusted value of q differs very little from its unadjustedvalue. Of course, the actualtimeseriesof adjusted = d, + {it differsfromthe unadjusted cjit cht series and, for some firms in the sample, the difference between d, and'-i is significant. To compare our findingswith other studies of q, we plot in figure2 the average value of q (unadjusted)for the years 1960 through 1977, and the economy-widevalues of q reportedfrom three sources: (1) the Economic Report of the President(1978), (2) the year-endnumbersin von Furstenberg(1977),and (3) the averageq values reportedin Tobin and Brainard(1977). We have also plotted the time series of adjusted values of q, averaged over our firms, from our study. The relatively constant value (approximately1.5) indicatingthat the capitalizedrents, earnedby firmsin our sample, have been sufficientto keep the average firm's marketvalue approximately50%above the replacementcost of its assets. Figure 2 also indicates a high degree of correlationbetween
  25. 25. 24 Journal of Business the q as we have measuredit and each of the other methods, although there are consistent differences between each of the estimates.20 Whataboutthe distribution q across firmsand industries?Figure3 of presents histograms for adjusted q across firms for the years 1960, 1965, 1970, and 1977. From these plots we see that the distributionof adjusted q ratios was approximatelyunchanged. The only apparent change is a reductionof some of the extremely large values of q over time. As we have previouslynoted, largeq values shouldbe associated with either significantmonopolyrents or with rent resultingfrom some special factors employed by the firm, all of which influence market power. In table 4, industry averages are listed in ranked order of overall average adjustedq. Many of the industries with the highest q values contain firms successfully marketing differentiatedproducts (e.g., cereals, drugs, cosmetics) or having strong patent protection (e.g., photo, drugs).Some industriescontainingfirmswith largemarket shares also rank highly, althoughsuch firms are scattered throughout table 2,21 and we will test this explicitly below. We have suggestedthat low values of q are associated with a relatively competitive market structure,a tightlyregulatedmarketstructure,or a dying-industry firm, and a casual reading of table 4 appears to confirm this. Steel and primary metal manufacturersrank low, perhaps reflecting the depressed natureof these industriesrelative to foreign substitutes. Also, the regulatedsector, for example, electric utilities, has relatively low q values. Furthermore,many firmsin other industries(e.g., petroleum refining)which are regulated in some form are noticeably below the upper ranges of the distributiondespite the conventionalwisdom concerning the oligopolistic nature of their business.22 Finally, as a test of significance,we examined the adjustedaverage q ratios for individual firms to see whether the monopoly power as measuredfrom the data was significantlyabove the theoreticalcompetitive level of 1.0. While the individualyear-by-yearq values can be thought of as independentdrawingsfrom a populationwith unknown 20. These other procedures, used to calculate q for the economy, have employed differenttechniquesto measureeither aggregatemarketvalue or aggregatereplacement cost and are not quite comparablewith our results. For example, both the Council of Economic Advisers and von Furstenbergproceduresuse flow of funds and other data aggregatesrather than estimates for a sample of individualfirms, and, in fact, their measures of replacementcost appearto be more reflective of reproductioncosts, for which much of the effect of technicalchange is absent. Such an omission would push measuredreplacementcost up and measuredq down. 21. Anotherreasonfor ranking high on the list mightbe a unique sales and marketing not organization easily replicated(Avon, IBM). A reason, not includedin the text, for rankinglow mightbe the ability of suppliers(e.g., unions) to appropriate some of the rents earned in output markets. 22. In severalcases, the numberof samplefirmswithina given industryis quite small. Some care is needed in makingsignificantstatementsconcerningrelativemarketpower in these cases.
  26. 26. -y-rrn-rr 90 o~ O,F~rT ~ ~~ ~ ~~ 0 In~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 t Hin?'~~~~~~~~~~~~i 0 o0 lo lo o * l L -O N 7 V % swji CIlI T*-I o C % I :A :- 0 Ca s~~~~~ 0~~~~~~~~~~~~~~~C p4 2'2~~~~~~c " 0~~~~~~~~~~ ~ ~ 00~I C4N swij o C!~N 0 2~~~~~~~~~~2 Li 00 t 0~~~~~~~~~~~~~~~CC Ci C? 40 sw(j! t? 0 L [ C li = C) I0O% 0I0n N 0 00 aW0 SWii 00j0 % 25
  27. 27. c Cl X "'t CN 0 W) "T X r,4 "T (ON (14 t- 0 0 W) el ON"It m aN c C C cli en en OC) cli C C c aN ,,t cq = W) "It INC M C) "T cl, CD c a W ,,t t-- 00 "It "It w 't W Nt ON (ON W) m m W aN "T m cq C14 cq m cq 0 tC14 "t = W W) ON W W,-tt "T c-, Rt ON 0 -4 m eq W) CN W W m 'Itt "It Itt o w c c a, w ,,t "'t kn m W) C) aN (7N= CN aN W - - C C m "t m M W (7N (ON W - t,- C) m - - aN - m "t t- m r- c (7 c t- W c cli "It t__ tl- en kn cq - 00 C 00 OC) "t a cp ,,t en Cl kr) kn tl- W) "It m m C 0 kr) t- c c C) Cf) en c en ON en m C) 't ON " en cq W) c en ON CD c en aN - OC) en W) m cl 00 O ,,t M C W) (14 - c en C - W) cl It 'IT en en c c en 00 - It 00 0 00 te) cq r- ON en (ON C) ON - W (7 C) m C) El kn CD ON kr) C c (7N CA " ON ON t- "It 't en en "It Cf) en t__ 00 (ON ON C ON r- 0 (1) Cd ( 4-0 00 C's C) ce cd Cd w C) ,,t C) - M (ON c C r- ON- t__ c r- o 'It "t llt W) ,,t kn c so "t r- - c m t- "t a, W ,t 1%c c tm aN ON W)m ,,t M M (7N r- "T m W) 't w Nt (Ii (= (ON " ,,t - ,,t cf & cli Ei 0.) 0 C)U,W,) u Cd m 0 u = U cd El 0 W I.- O to 1-4 26 t- tl- en cq tn kr) (7Nt- 00 M It "T cq m - "It "It " t- Cfi lr cli C*l U W 0 (Ii (Ii C 00 0 0 0-4 r- = IRll ,I:11-t 111: "ItI-qen V: t-: 't Nt c CD w w cl 'Itt 10 r- W ,,t W t__ W) t- tl-- W) "It 't 't W) cli cli cli c m r- r- 00 tc "T - a "'t c 00 -,--q M _ O 13 lr C cli > r- "t C"! rl O '15 cd El m v) ,0 z 00 cols, cd (L) Ctff = El Cd 0 C) 0 El uw 0 X ON kn cd 0 kn 24 - 8 m v) 0 cd 0 El cd C,3 z 6, El u P u ,: 4 u 4. w 4. O m 4.) 0 r" 0 z El IL) u a m r. u ;D 7 tm 0 in. 'IC m - c w c,3 1-4 't % C,3 El kn m
  28. 28. 27 Tobin's q Ratio and Industrial Organization mean, the distributionis not known, and the sample size of 18 years may not be sufficient to use a t-statistic for significance tests. Consign test to test the sequently, we employed a one-sided nonparametric null hypothesisHo:qi = 1 againstthe alternativehypothesisH1:qi > 1. At the 5% level, it was found that 159 of the 246 firms had q ratios significantlyabove one, while for the others, the estimated values do not permit us to rule out the possibility of no monopoly rents. V. Comparisons with Other Measures of Monopoly Power In this section, we examine the empiricalrelationshipbetween q and two of the most commonly used measures of monopoly power, the Lerner index and the four-firm concentration ratio. The four-firm data (based on value of shipments)was taken from concentration-ratio the 1972 Census of Manufacturers (U.S. Departmentof Commerce industriesby four-digitSIC code. 1972)for each of the manufacturing Includedon the COMPUSTAT tapes are the four-digitSIC codes, but, in some cases, adjustmentswere made on the tapes to account for a firm doing significant business in several industries with, say, the same three-digitcode. For example, if a firm was significantlyinvolved in industries 2011, 2012, 2013, . .. , the recorded SIC code would read 2010. Consequently,it was necessary to construct averages (weighted by value of shipments)for all three-digitcodes, two-digitcodes, and so forth. For each firm, there is an associated concentrationratio representing the share of value of shipmentsin 1972of the four largestfirms in its "industry." Lerner indices can be constructed using firm-specificdata alone. Because we lack adequatemarginalcost data, we assume that average variable cost equals marginalcost. If the firmproducesa homogeneous product, Lerner's index will be given by P -MC P _P - AVC P PQ - AVC PQ Q Sales-OperatingExpenses Sales Letting Lit and CRit denote, respectively, Lerner's index and the four-firmconcentrationratio for firmi in year t, we regressedqit on Lit for the entire 1960-77 period and qi,1972 on Li,1972and CRi 1972for the year in which census data was available. The results are reported in table 5. All of the coefficients have the predicted positive sign. The Lerner index is, from all three regressions, an importantcontributortoward explaining monopoly and Ricardian rents. The concentration ratio, however, seems to have no significantrelationshipwith q. Evidently, high q's can occur in concentrated or unconcentratedmarkets and,
  29. 29. 28 Journal of Business Table 5 Regression Results Regressions 4it = q i,1972 q i,l972 Indices i = 1,. 1.03 + 3.10Lit (19.59) = 1.46 + .27 CR i,1972 (0.63) = .19 + 8.28 L i,1972 + .04 CR i,1972 (11.27) (0.11) NOTE.-Numbers 246 t = 1960,. r2 1977 .08 i indexes manufacturing-sector firms .01 i indexes manufacturing-sector firms .29 in parentheses are t-values. conversely, low q's, indicatingno significantmarketpower, can occur in markets that have high degrees of concentration. The values of r2 in these regressionsare not unreasonablefor crosssection regressions. But, recallingthe basic Propositionof Section II, we see that Lerner's index only provides a lower bound for q which also dependson the ratioof marginal averagecost. The lower bound, to then, will be lower for firmswith high fixed costs and/oreconomies of scale. If actualq moves with the bound, we shouldexpect it to be lower for firmswith higherdegrees of scale economies or higherfixed costs. In these cases, the Lerner index is inadequate in explaining market power because it does not recognize that some of the deviation of P from MC comes from either efficient use of scale or the need to cover fixed costs and does not contribute to market value in excess of replacementcost. An example of this phenomenonoccurs for regulated utilities. Their Lerner indices are significantlyhigherthan the average for all firms,and yet they have q ratios amongthe lowest in the sample. These are firms with large capital investments, high fixed costs, and significantscale economies duringthe study period. As a direct test of the Proposition presented in Section II, we construct the- statistic [1/(1 - L)] [MC/(AVC + AFC)] for each firm in each year of the studyperiod. Accordingto the Proposition,this should be a lower bound for q. Assuming, again, that marginalcost equals averagevariablecosts, and, in addition,that total fixed cost in a given year equals an interestrate (an annualization factor)times replacement cost, we test the hypothesis Hl: qi > i 1)AVC ) AVCi + rRC ) 1 (1 -Li against the null hypothesis = HO:qiq I I I -L Li AVC, AVCi + rRCiJ Table 6 reportsthe results of performing nonparametric test of a sign the hypothesis for the values r = .05, .10, .15 and for an interest
  30. 30. Tobin's q Ratio and Industrial Organization Table 6 29 Lower Bound Tests for q* Interest Rate r (%) 5 Firms with q above theoretical bound at 5% level (N) Firms with di above bound (%) 10 15 5-15 126 150 168 152 61 67 73 71 *Test of q ? (1/1 - L) (MCIAC),where L Lerner index, MC Average cost averagevariablecost + r replacementcost. marginalcost, and AC- starting at .05 in 1960 and rising uniformly to .15 in 1970. We list, for each value of r, the number of firms for which Ho is rejected in favor of H1 and the percentage of firms whose adjusted q ratio, di, is above the hypothesized bound, evaluated at average values of its components. The majority of firms have average adjusted q ratios that exceed the bound. The test results indicate that Ho is rejected with a frequency much greater than chance, suggesting that the proposition indeed holds. As is shown in table 6, these results are relatively unaffected by the assumptions on the cost of capital. VI. Summary and Conclusions We have developed in this paper a model which enables us to examine the extent, distribution, and history of monopoly and quasi-rents in the industrial sector. This model uses the linkage between financial price data and accounting data to construct empirical measures of supercompetitive market power for individual firms. The work grows out of the pioneering work of Tobin, who recognized that the relation between market value and replacement cost is crucial in the investment decision making process. Our results show a wide dispersion of market power across firms and industries. For the economy as a whole, the raw data is consistent with findings elsewhere that market value as a percentage of replacement cost has declined over the past 2 decades. After adjusting for economy-wide effects and firm effects that do not influence market power, we find that, on average, market values have been approximately 50% above replacement costs over the period 1960-77. We also have shown that the dispersion of monopoly power has not changed significantly over this period. Our results indicate that the sectors of the economy that have q ratios at the high end of the spectrum are often those with relatively unique products, unique factors of production, and so forth, all of which contribute to monopoly and/or quasi-rents. At the low end, we find either relatively competitive, tightly regulated, or dying industries.
  31. 31. Journal of Business 30 We have also examined the relationship between q and two frequently used measures of monopoly power-the Lerner index and the four-firm concentration ratio. We found that while the Lerner index contributed toward explaining q, the concentration ratio seemed to have little significance. We must stress at this point that all these results are subject to the usual caveats concerning data availability and quality, and improvements in these areas would greatly aid future research. Appendix It is useful to examine the impactof technical progressand its relationshipto marketvalue and replacementcost. Initially,let us definereplacementcost as the capitalexpenditurenecessary to producethe identicalproductline with the most efficient technology. To be explicit, let Ktbe the current,time t, cost of a machinewhichproduces one unitof the productin a perpetualflow. Suppose, also, thatCt is the variable cost streamof the machineand letpt be the currentproductprice. We consider machinesin a putty-clayformat;once installed,unit operatingcosts are fixed. In a competitive marketfor new capital goods, we must have market value Mt= (pT 00 = - r(T-t)d r - -Pt dr Ct)e (AI) Ct/r CtIr =Kt, or qt = MtlKt = 1. If the cost streams, {Ct} and {Kt}, are specified, then the productprice will adjust throughthe supply curve to bringabout the equilibrium. In particular,with Kt and Ctlr fallingover time, discountedprices must fall as well. (Since Kt + Ctlr > 0, eventuallypt must fall at a decreasingrate.) Whathappensto the q value of vintageequipment?Considera machinebuilt at time s as viewed at time t. Its market value is given by sMt = (PT - = Pt - (A2) Cs)e-r(T-t)d CsIr. By definition, replacementcost is the cost of the most efficient technology, hence sRt = Kt. It follows that sqt = Ct/r)/Kt (A3) Cs/r)/Kt sMtlsRt = (Pt- < (Pt - = tlKt = qt = 1 since operatingexpenses are falling.In other words, when we are not replacing old equipment,with inefficientoperatingcharacteristics,then q, as we would expect, is less than unity.
  32. 32. Tobin's q Ratio and Industrial Organization 31 Notice, though, that if technical progress is capital augmentingand there is no improvementin operatingcosts, then Cs = Ct; 8Mt = Mt and sqt = sMtlKt = MtlKt = qt = 1. It is tempting to fall into a trap suggested by the following conundrum.Suppose thattechnicalprogressoccurs as variablecost reductions and new machine costs are actually the same as replacement costs of old machines. It is not now possible for the measuredq for old equipmentto be lower than its true value?The answer, as we have seen, is clear. As long as the new machineis economicallymore efficient, it shouldreplacethe old machine. Thus the ratioof the old machine'smarketvalue to the new replacementcost is the trueq. If new machineshave a lower operatingcost, then resultingproduct prices bring currentq to unity and measuredq will be correct. Technicalprogresswhich reduces operatingcosts, which are not expressible as capital augmenting,will bias q downward.Keep in mind, though, that the division of technical progress in this fashion is somewhat arbitraryand if the productionstructurepermitstechnicalprogressto be put in a capitalaugmenting form, q will be forced to unity for competitive firms. An alternativedefinitionof replacementcost has the virtue of maintaining the equalityof competitiveq with unity. Let us define replacementcost as the cost of acquiringthe same profitstreamwith the most efficient,that is, the cost minimizing,technologyfor producingthe same productline. Under this definition, with syt units of new capital,we can duplicatethe profitstreamof vintage capital, where sYtmt = sMt (A4) the Superscripting alternativedefinitionby a prime, we have sqt = sMtlsytMt = MtlKt = qt = 1. (A5) Hence, as long as the productline is produced,q' = 1 for competitivefirms.Of course, q can exceed unityby monopolyand/orfactorrentsfor noncompetitive firms. The alternativedefinitionof replacementcost is more suitable for our purposes than the originalone, but direct data on it is not readilyavailable.At any rate, our proceduresare based on accountingdata on dollar investmentflows and assume exponential technical progress. Insofar as yt declines geometrically, the cross-sectional results should be somewhat immuneto these problems. Furthermore,our results on cross-sectional comparisons of q will be robust to the extent that there is not too much cross-firmvariation in the relative proportionof capital and variable cost technical progress. Since all firms respond to the same factor price patterns, the endogeneity of technical progress lends some a priori supportto this view. The second definitionis also superiorto the originalone because of a more serious flaw. The choice of an efficient capital stock may not be unique. In particular, there could be a family of efficient choices, those with lower operating costs having higher initial costs. This makes the first definition somewhat arbitrary.The alternativedefinition,though, gives a unique value to replacement cost. However, in the context of our paper, with technical progress assumed to be capital augmenting,our first definition will suffice. The discussion in this Appendixis intendedto clarifyalternativeapproachesto this issue.
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