Gomes2001_FinancingInvestment

8/3/2019 Gomes2001_FinancingInvestment

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American Economic Association

Financing InvestmentAuthor(s): Joao F. GomesSource: The American Economic Review, Vol. 91, No. 5 (Dec., 2001), pp. 1263-1285Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/2677925

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Financing InvestmentBy JOAo F. GOMES*

We examine investmentbehavior whenfirms face costs in the access to externalfunds. Wefindthatdespitethe existenceof liquidityconstraints,standard nvestmentregressionspredict that cashflow is an importantdeterminantof investmentonly ifone ignores q. Conversely,we also obtain significantcashflow effects even in theabsence of financialfrictions. These indings provide supportto the argument thatthe success of cash-flow-augmented nvestmentregressions is probably due to acombinationof measurement rror in q and identification roblems. (JELE22, E44,G31)

A recurrentpuzzle in the investment litera-ture is that measures of Tobin's q and of thecost of capital appearto have a negligible im-pacton investment.A recentstrandof empiricalwork has sought to investigate this puzzle bystudying the interaction between investmentand financing decisions at the plant and firmlevel. The findings of these studies seem tosuggest thatfinancialconstraintsplay an impor-tant role in shaping corporate investment: (i)cash flow is highly significant in investmentregressions; and (ii) small firms appear moreliquidityconstrained han large ones. These mi-cro data sets have also allowed researchers ouncover a wealth of new empirical regularitiesabout firms and their investment decisions: (i)investment s lumpy, periods of low investmentare followed by large investment spikes; (ii)small firms grow faster and invest more thanlarge firms;and(iii) entryand exit ratesareverylarge.We seek to understandthese facts using amodel of investmentbehaviorwhere heteroge-neous firms face costly external finance. In thisenvironment irms seek to maximizetheirvalueby making three interrelateddecisions: (i) theymust choose whetherto participateor not in the

market; f they decide to participate hey must(ii) choose how much to invest; and (iii) how tofinance their investment. This model success-fully replicates all the stylized facts describedabove, thus providing a useful laboratory toinvestigate the role of financing constraintsandtheir mplications or the performanceof empir-ical investment equations.Using the model's stationarydistributionoffirmsto run standard nvestmentregressions,weobtain four mainfindings. First, the existence offinancialconstraintss not sufficientto establishcash flow as a significant regressor n standardinvestment equations, beyond q. In the contextof a fully specified model, the effect of financialconstraintsshould be already included in themarketvalue of the firm and thus should also becapturedby q. Second, financingconstraintsarealso not necessary to obtain significant cash-flow effects. We show that it is possible toconstructexampleswhere cash flow addssomepredictive power to investment equations, evenin the absence of financial frictions. Third,as Thomas J. Sargent (1980) and Matthew D.Shapiro(1986) documented,we findthat,in thecontext of these general-equilibriummodels, aspurious correlation between investment, cashflow, and output is likely if one neglects theeffects of underlyingshocks. Clearly this im-plies that focusing on these reduced-forminvestment equations is quite problematic.Fi-nally, we studythe effects of alternative ourcesof measurement error in the model. As ex-pected,we findthatusing incorrectmeasuresoffundamentals an lead an econometrician o as-sign a much larger role to cash flow in thereduced-form investment regressions. These

* The Wharton School, University of Pennsylvania,3620 Locust Walk, Philadelphia,PA 19104, and CEPR.(e-mail:[email protected]). would like to thankAndy Abel, Rui Albuquerque, Marty Eichenbaum, Fran-cisco Gomes, Jeremy Greenwood, George Hall, HugoHopenhayn,Per Krusell,Sergio Rebelo, RichardRogerson,Amir Yaron, two anonymousreferees, as well as numerousseminar participants or all the valuable comments. Finan-cial support rom JNICT andthe Bank of Portugal s grate-fully acknowledged. Any errorsare mine. 1263


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1264 THEAMERICANECONOMICREVIEW DECEMBER2001findings highlight the enormous difficulties inusing standard nvestment regressions in prac-tice, and they cast serious doubt on the commoninterpretation f cash-flow effects in the data asevidence of financingconstraints.This paper is organized as follows. Section Iprovides a brief overview of recent empiricalfindings about nvestmentbehavior and its rela-tion to financialvariables. Section II describesour economic environment. Section III detailsboth the calibrationmethods and characterizesthe competitive equilibrium generated by themodel. The theoretical mplicationsfor the em-pirical investmentequations are then examinedin Section IV. Section V summarizes ourfindings.

I. Investment nd FinanceA. InvestmentBehavior

Investment s a central macroeconomicvari-able. Its fluctuations account for a large frac-tion of the cyclical volatility of outputand in-come, and most economists link high rates ofinvestment to long-run economic growth. Un-fortunately,understandingnvestmentbehaviorhas proved to be a very difficult task (seeAndrew B. Abel, 1980; Abel and Olivier J.Blanchard,1986). Earlierwork focused on rep-resentativeagent frameworkswith convex coststhat smooth investment over time (Dale W.Jorgenson, 1963;JamesTobin, 1969;Robert E.Lucas,Jr. and EdwardC. Prescott, 1971;FumioHayashi, 1982, among others). Empiricalworkbuilt directly on these theories to estimateempirical investment equations, using bothaggregate and firm-level data (George vonFurstenburg, 1977; Abel, 1980; Lawrence H.Summers, 1981).The empirical performance of these earlymodels was disappointing, however, and at-tention shifted recently towards alternativetheories emphasizing fixed costs and irrevers-ibilities (for example, Sargent, 1980; Abeland Janice C. Eberly, 1994; Avinash K. Dixitand Robert S. Pindyck, 1994). A significantimplication of this new theoretical approachis that investment should be "lumpy": signif-icant amounts of investment, or disinvest-ment, take place in a relatively shortperiod oftime, while most periods are characterizedbyonly minor changes to the existing capital

0.180.160.140.12

0.10.080.060.04\0.02

1 3 5 7 Ye (rank) 11 13 15 17

FIGURE 1. FIRM-LEVEL INVESTMENT SHARES

stock. Empirical evidence provides supportfor this approach. Figure 1, adapted fromMark Doms and Timothy Dunne (1998),ranks the average rates of investment for over12,000 plants for the period 1972 to 1988.The concentration of plant-level investment isclear: about 25 percent of investment spend-ing takes place in one year and on averageabout half of a plant's total investment takesplace during a three-year period.A consequence of these models is that simpleaggregation heoremsno longerhold. The largenonlinearitiesn investmentbehavior mply thatthe cross-sectional distribution of firmlplant-level investmentmay affect aggregatevariables,which requires modeling firm heterogeneityexplicitly (Ricardo J. Caballero and EduardoEngel, 1994; Caballeroet al., 1995; Abel andEberly, 1996; Marcelo Veracierto, 1997; Rus-sell Cooperet al., 1999).

B. FinanceIn contrastwith the predictionsof the FrancoModigliani and MertonH. Miller (1958) theo-rem, most firms seem to preferinternalsourcesto finance investment.Accordingto StephenA.Ross et al. (1993), about 80 percent of all fi-nancingis donewith internallygenerated unds.Explanations or this behavior usually highlightthe role of informationasymmetries StewartC.Meyers and Nicholas S. Majluf, 1984) andagency issues (Michael C. Jensen and WilliamH. Meckling, 1976) in raising the costs of ex-ternal funds.In a detailed study, StephenM. Fazzari et al.

(1988) find that low-dividend-payingfirms (apriorimore likely to be financially constrained)are generally smaller, invest more, and grow


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 1265faster than high-dividend irms.They also havehigher cash flows and higher average q's.In addition, reduced-form nvestment equa-tions find evidence of highly significant cash-flow effects while, on the other hand, Tobin's qappearsto have only a marginal mpact on in-vestment.A numberof authorshave interpretedthis as evidence supporting the existence ofsignificant finance constraints, particularly orsmall firms.Several otherstudiescast doubt on this inter-pretation however. From a theoretical stand-point, workby Sargent (1980), Shapiro (1986),and, in a somewhatdifferentcontext, Peter M.Garber and Robert G. King (1983), suggest anumberof potential problems with the estima-tion of reduced-formequationsfrom structuralmodelsof firm and investmentbehavior.In par-ticular, they show that when the underlyingshocks to output and cash flow are positivelyautocorrelatedt is possible to obtain strong,butquite spurious, correlationsbetween these vari-ables and investment when one ignores morestructural nformation.On the empirical side, work by SimonGilchrist and Charles P. Himmelberg (1995),Jason G. Cummins et al. (1998), andTimothyErickson and Toni M. Whited (2000) arguethat, at least in some cases, the observedcash-flow effect in earlier studies merely re-flects the fact that cash flow might containinformation about the firm's investment op-portunities, otherwise not reflected in themeasure of Tobin's q being used. Althoughtheir methodologies and results differ some-what, two common findings emerge.' First, itis clear that serious consideration of mea-surement issues assigns a much larger roleto fundamentals in the estimated equations.

Second, both in Cummins et al. (1998),Erickson and Whited (2000), and even insome subsamples in Gilchrist and Himmel-berg (1995), the cash-flow effect actuallydisappears: cash flow adds no signifi-cant predictive power to the investmentequation.This debate about the significance of cash-flow augmented nvestment regressions is verydifficult to understand,however, due to the ab-sence of a solid theoretical structure behindthese reduced-formregressions. Our main goalhere is to provide a theoretical backgroundagainst which one can betterunderstand heseresults.

II. Economic EnvironmentA pattern that emerges from the evidencediscussed is one of substantial irmheterogene-ity across a number of different characteristicssuch as firm size, growth, investment, and fi-nancing patterns.It seems, then, important hatour frameworkbe consistent with this and thusable to produce a well-defined distributionoffirms that provides a reasonable description ofthe data.The environment is an equilibrium variantof the standard neoclassical model of invest-ment augmented to include financing con-straintsat the firm level as in William A. Brockand Blake LeBaron(1990) andentryandexit inthe tradition of Boyan Jovanovic (1982) andHugo A. Hopenhayn 1992). Financial nterme-diation is not modeled explicitly however. In-stead we proceedin the spiritof workby S. RaoAiyagari and Mark Gertler (1991) and JavierDiaz-Gimenezet al. (1992), andsummarize hiscostly activity with a simple functional form

thatcaptures he basicnotion that external undsseem to be morecostly than internalones. Thisis sufficient to make internalfunds "valuable"for firms.The economy consists of three sectors:households, financial intermediaries,and pro-ducers. Householdsare representedby a singleagent maximizing lifetime utility. Incomecomes from wages and dividendson the sharesthat the household holds in every firm. Firmsproducea single outputthat can be transformedin eithercapitalor consumptiongoods, combin-ing labor serviceswith capital goods. Firmspaydividends directly to the consumer but require

1Briefly, Gilchrist andHimmelberg(1995) adopt a pro-cedure similar to that developed in Abel and Blanchard(1986) to constructan alternativemeasure of fundamentalsthat is then used in standardnvestment regressions nsteadof average q. Cumminset al. (1998) use earnings forecastsfrom the I/B/E/Sdata set to constructan alternativemeasureof fundamentals. This is then used in both the standardinvestment equations and also in some semiparametric e-gressions. Finally, Ericksonand Whited (2000) develop avery sophisticated conometricmethodologybased on high-orderGeneralizedMethods of Moments (GMM) estimators,specifically designed to handlemeasurementerror. Minordifferences also exist in the definition of variables andsample construction.


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1266 THEAMERICANECONOMICREVIEW DECEMBER2001Exitandsell capital... .... ._................ .......

E stay, --,--Q(ztzt- l) t

Observe Investment:-.E:....,...~~ ~ ~ ~ ~ ~ ~~~ ....... ........ . .....socks

enter stayotit..E-.-.... . . . .-..................... ................................t ~~~~~~~ ~ ~ ~~~~~~~~........- .- .S-s .................................................................t +1

FIGuRE 2. TIMING OF EVENTS

the servicesof financial ntermediaries o obtainadditional funds. Financial intermediaries arealso summarized n a single agent that providesthese services at some cost.A. Firm Behavior

Production is carriedout in all periods by acontinuum of firms. Figure 2 provides agraphical description of the timing of the de-cisions made by firms in this economy. In anygiven period each incumbent chooses (i)whether to exit the market or continue pro-ducing, and, if it stays; (ii) how much toinvest; and (iii) how to finance the investment(internal or external funds). Incumbent firmschoose to exit at the start of the period beforeany current variables are observed and beforethey make any other decisions. Firms that exitsell all their assets, hire no labor, and earnzero profits.In every periodthere is also a continuum ofpotentialentrants hat decide whether or not toenter the market.Entrantschoose to enter alsoat thebeginningof theperiodbeforeanycurrentvariables are observed.Productionrequires two inputs: capital, k,and labor, 1, and is subject to an individualtechnology shock, z. Firms hire labor at themarketwage rate w > 0 and discount futurecash flows by a factorof 13E [0, 1). The spaceof inputs is a subset of the space of (nonnega-tive) realnumbers,SCX _TC 22 . The stochas-tic process for this shock has boundedsupportZ = [z, z], -oo < z < -z < oo. Alsodefine $z and Sk as, respectively, the minimalsigma-fieldsgeneratedby Z andSC.Productionof the single good is carried out by each firm

according o the production unction F: Jf X SX Z -> 9,. Assumption 1 summarizes theconditionsimposed on F.ASSUMPTION 1: Theproduction unction F:Jf X S_ X Z -> + has thefollowing proper-ties: (i) strictly increasing, strictly concave,twice continuously differentiable, homoge-neous, and satisfies the Inada conditions; (ii)Vh > 0, F(hk, hl, z) < hF(k, 1, z).

Withoutdecreasingreturns o scale [part ii)]theindividualdecisionrules andthedistributionof firms would not be well defined. We alsoassume that there is a fixed cost of production,f ' 0. This cost must be paid every period thefirmremains in the market.Assumption 2 below concerns the idio-syncratictechnology shocks. We use z' to de-note the value of next period level oftechnology.ASSUMPTION 2: (a) Incumbents'shocks (i)are uncorrelated across firms, and (ii) have acommonstationaryand monotone(increasing)Markov transition function Q( z', z): Z X

-> [0, 1] thatsatisfiestheFellerproperty; b)entrantsdrawtheir initial level of technology n-dependently rom a common distribution(p( ).

Without idiosyncraticshocks the productionsector could be consolidated nto a single pro-ducer,as all firms would notonly have the samedecision rules, but would also make the samechoices.Forsimplicity t is assumed hatthe sto-chasticprocessfor each firm follows a commonMarkovprocess. Monotonicityof the transitionfunctionguaranteeshatprofitsare increasing nthe current hock,a result thatwill proveusefullater.Assumption2 also determines he distribu-tionof shocks or newfirms.These areassumed obe drawnafterthe entrydecisionis made,poten-tially implying substantialheterogeneityn pro-ductivityacrossall new entrants, fact consistentwith the evidence in Dunne(1994).We can now summarize the static decisionsof the firm,thus simplifying the dynamicdeci-sion problembelow.* Profits(1) 7r(k, z; w) = max{F(k, 1; z) - wl -f }.

1'0


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1268 THEAMERICANECONOMICREVIEW DECEMBER2001costs. The last term is the expected continu-ation value, allowing for the exit decision.Firms will exit when expected profitability isbelow the marketvalue of its assets:

(7) p(k', z'; w)Q(dz'Iz) < (1 - 6)k'.

In what follows we will focus solely onstationary equilibria, where all prices andaggregate quantities as well as the distribu-tion of firmsacross states are constant. Belowwe show that such equilibrium indeed existsand is unique. Thus we will assume thatw = w.The fact that the exit decision is incorpo-rated in the solution of the dynamic problemof each firm together with the finance costfunction complicates the dynamic program(6) considerably. Nonetheless one can showthat a solution to this problem exists andestablish some useful properties for the valuefunction p(k, z; w).PROPOSITION1: There is a unique unctionp(k, z; w) that satisfies (6).PROOF:See Gomes (2000).PROPOSITION2: The value function p(k, z;w) is (i) continuous and increasing in (k, z),and (ii) continuous and strictly decreasingin w.PROOF:See Gomes (2000).

Proposition 1 guarantees the existenceof a value function p(k, z; w) that solves(6), while Proposition 2 establishes some ofits properties. Associated with this solutionthere are two decision rules concerningcapital accumulation and the exit decision,denoted k(k, z; w) and x(k, z; w) respec-tively. Both are computed in the process ofsolving the dynamic problem of the firm.Capital accumulation is described by the con-dition

(8) k(k, z; w) = min arg max{7T(k,z; w)k -o

- i(k, k') - A(k, k', z; w)

+ /3 max((I - S)k', p(k', z'; w)

X Q (dz', z)Given the structureof the problem,the max-imizer on the right-hand ide of (6) need not beunique.Equation(8) states that a firm choosesthe valuethatdoes notrequireexternal inance.2Intuitively, f borrowingdoes not (strictly)raisethe value of the firmit is not used.Since exit takes place before the shock isobserved, firmsknow in advance whethertheywill choose to exit or not in the nextperiod.Exitis thereforecompletely determinedby the cur-rent state and can be summarizedby a thresholdvalue for the idiosyncraticproductivitylevel.The exit decision can be describedas follows

(9) x(k, z; w) Io z > z* (exit)where(10) z*(k, z; w)

= min inf z: p(k', z'; w)

X Q(dz'jz) (1 - )k'}JZ.Intuitively, conditions (9) and (10) formal-ize the idea that firms choose to stay only iftheir future prospects (as measured by theirexpected value next period) are good enough2 Only two solutions can exist for each state, one withand one withoutexternialinance. Clearlyif the value of thefirm is the same in both cases and the value function isincreasing in capital, then the optimal investment choice

must be higherwith externalfinance.Technically, (8) pro-vides a measurable selection of the optimal policycorrespondence.


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 1269to justify the fixed cost of operating the firmnext period. Because shocks are positivelycorrelated, this is only true if the currentlevel of productivity is above some thresholdz. Propositions1 and 2 characterize he solutionto the individual problem of each firm for agiven wage rate w. The equilibrium evel of wis uniquely determinedby the free-entrycondi-tion:(I11) p(0 z; w)(pdz) c< o.This condition must hold with equality if entryis positive. In this case Proposition2 guaranteesthatthere s a uniquevalue of w that solves (11).The exact level of entry, denoted by B, is thendetermined by the market-clearingconditionsbelow.

B. AggregationWith the description of individual firmbehavior complete we can now characterizethe aggregate variables for this economy.

Since each firm can be describedby its currentindividual tate (k, z), we can summarize he ag-gregatedistribution f firms with a measurede-fined over this statespace.Formally we define the measure t such thatV(k, z) E J X Z, pt(k,z) denotes the mass offirms in the state (k, z). For any set 0 = (X,3) E S~k X ,z the law of motion for thismeasure t is given by(12) Ct(e)

(T(O, (k, z)) yt(k, z), if k> O=T(O), (O, z))yt(O, z)

+ B x(K)v(dz)Q(dz'lz), if k = 0

with(13) T(O, (k, z))

I X(X()x(k, z; w)Q(dz z),3

and(14)

01if k k, z; w) E X,x(Xk)= if k(k,z; w) ? X.

Condition (12) specifies the law of motionfor the aggregate measure of firms: next pe-riod's measure is determined directly fromcombining the surviving firms with entrants(which have zero capital at the moment ofentry). Condition (13) describes the law ofmotion for the individual state of survivingfirmsby combining the optimal decision rulesconcerning capital accumulation and exit. Itcomputes all the conditional transition prob-abilities in the product space SCX Z, wherethe conditioning event is that the firm sur-vives until next period. Naturally in a station-ary equilibriumwe expect that p' = t = pt*.The invariant distribution pt summarizesthen the distribution of firms in a stationaryindustry equilibrium.With this definitionat hand it is straightfor-ward to characterize the aggregate quantitiesthat will be used below to state the market-clearing conditions. These are the (net) aggre-gate supply of final goods, the aggregatelabordemand,total profits,and the aggregateinvest-ment, definedrespectively as

(15) Y(pt,B; w) = (y(k, z; w) -f)X x(k, z; w),u(dk, dz) - Bf,

(16) L(pt, B; w)| l(k, z; w)x(k, z; w),u(dk, dz)

+ B 1(0, z; w)sp(dz),


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1270 THEAMERICANECONOMICREVIEW DECEMBER2001

(17) Hl(Pt,B; w)

7r(k,z; w)x(k, z; w),u(dk, dz)

+ B ir(O,z; w) p(dz),

(18) I(pt, B; w)

i(k(k, z; w), k)x(k, z; w)l(dk, dz)

+ B k(O, z;w)p(dz).

Similarly, total intermediationcosts for thiseconomy are given by the function(19) A(y, B; w)

| A(k, k(k, z; w), z; w)X x(k, z; w) (dk, dz)

+ B A(O, k(O, z; w), z; w)(p(dz).

Proposition 3 establishes that aggregatequantities are jointly linear homogeneous inthe level of entry B and the measure of firmsy. This property will be useful later when wecompute the competitive equilibrium of themodel.PROPOSITION3: All aggregate quantitiesY(,u, B; w), L(p-, B; w), H(/, B; w), I(/,B; w), and A(p,, B; w) defined aboveare jointly homogeneous of degree one in Band /.PROOF:See Gomes (2000).

C. HouseholdsThe model is completed with a descriptionof household behavior. Households are sum-

marized by a single representative consumerwho derives utility from work and consump-tion. Household income comes from wagesand dividends on the shares of existing firms.The household problem can be written as

(20) max Eo , I 'U(ct, 1 -It)c,l ,st (kt zt)-O t =0

s.t. ct + (Ptl(k,z)- dt(k, z))st(k, z)p,(dk, dz)

max{fpt(k, z), k}st-I(k, z)X p,(dk, dz) + wtlt,

where c is consumption,andflt(k, z), dt(k, z),andst(k, z) denote the price,dividends,and thefractionof sharesowned by the household,re-spectively. For convenience we assume thatdividends are paid just after shares are bought.Note that,since we arerestrictingourselves to astationarymeasure of firms ,u, the assumptionof a stationary equilibriumis implicit in thisformulationof the householdproblem.We sum-marize our (standard)assumptionsaboutpref-erences in Assumption4.ASSUMPTION4: Thepreference relation sat-isfies (i) 0 < 13< 1, and (ii) U(c, 1 - 1):+ X E-> Qk s strictly increasing, strictlyconcave, and twice continuouslydifferentiable.

Under these assumptions t is easy to estab-lish thatin a stationary quilibrium he discountrates for consumersandfirms are the same, andthe priceof a share,p(k, z), equalsthe value ofthe firm, p(k, z).PROPOSITION4: In equilibriumfi(k, z) -p(k, z) and ,B= P3.


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 1271PROOF:See Gomes (2000).

Since all aggregate quantitiesand prices areconstant, the consumer problem can then befurthersimplified into a static problem of theform(21) max U(c, 1 - 1)

c,10

s.t. c = wl +H(p, B; w),

which is a standard concave problem withinterior solutions given by two optimal deci-sion rules for consumption and labor supply,denoted respectively by C(w, Hl(p, B; w))and LS(w, Hl(y, B; w)).

D. Stationary CompetitiveEquilibriumWith the model complete we are now readyto state the conditions requiredto characterizea stationary competitive equilibrium for this

economy.Definition1: A stationary competitive equi-librium is a set of (i) allocation rulesLS(w, H(p, B; w)) and C(w, H(p, B;w)) for the representative household andk(k, z; w), l(k, z; w) and x(k, z; w) as wellas a value function p(k, z; w) for eachfirm; (ii) aggregate quantities Y( , B; w),L(p, B; w), H(p, B; w), I(p, B; w), andA(p, B; w); (iii) a wage rate w; and (iv) ameasure t of firms and a level of entry B,such that:* the consumer decision rules solve (21);* the firm decision rules and value functionsolve (6) for each firm;* the free-entrycondition(11) is satisfied;* markets clear:(22) Ls(w, H(it, B; w)) = L(g, B; w);(23) C(w, H(ji, B; w)) = Y(g, B; w)

- I(, B; w) - A(g, B; w);

* consistency: conditions (15)-(19) are satis-fied and the distribution t obeys the law ofmotion (12), with t = '.PROPOSITION 5: A stationary competitiveequilibriumwith positive entry exists.PROOF:See Gomes (2000).

III. StationaryEquilibriumComputing the competitive equilibrium inDefinition 1 involves three steps. First, weneed to restrict the model by specifying thefunctional forms assumed by the generalfunctions in the model. Then, as many param-eters as possible must be determinedeither bymatchingpropertiesof themodel to U.S. data orby using prior empiricalevidence. Second, be-cause exact analyticalsolutions are impossibleto obtain in this environment,we need to de-velop a numericalalgorithmcapableof approx-imating the competitive equilibrium up to anarbitrarily mall error. Gomes (2000) providesthe detailson this procedure.The finalstepis to

implement the numerical algorithm and com-pute the approximate stationary competitiveequilibrium.A. Calibration

We need to specify a functional formfor technology, one for the utility functionand another for the intermediation costfunction. We assume that a time period inthe model corresponds to one year, sincethe available data has yearly or lowerfrequency.

Preferences.-Since preferencesare not cru-cial to our analysis we will take a minimalistapproachand summarize household behaviorwith a momentaryutilityfunction similarto thatin GaryD. Hansen (1985):(24) U(c, 1) = log c + H(1 - 1).This function has the convenientpropertythatlabor-supplydecisions areindependent rom thelevel of wealth and from the real interest rate.Given this specificationwe only need to assign


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1272 THEAMERICANECONOMICREVIEW DECEMBER2001parametervalues to f3, the intertemporaldis-count factor, and H, which is determinedby thefraction of workers in the population. In thesteady state the real interest rate equals r =1/, - 1. Over the last century this value hasaveragedabout 6.5 percentperyear, thus we setf3 = 1/1.065. Since the shareof employed work-ers in the labor force equals about 60 percent,we choose this value for the parameterH.

Technology.-To completelyspecify the pro-ductiontechnologyof this economy we need tochoose a functional form for the productionfunction andthe stochastic process for the pro-ductivityshocks.We also need to assign param-etervalues for the investment unction,the sunkcost of entrantsand the fixed cost of production.We startby assuming that productiontakesplace in each firm according to a decreasingreturnsCobb-Douglas production unction(25) y = Ask kilI O < al + ak < l-With this specificationwe need only to assignvalues for ak and a,i, the two output elastici-ties.3To do this we need firstto determinate hedegreeof decreasingreturnsn theeconomyandthen one of the two elasticities.Using disaggre-gated data for manufacturing ndustries, CraigBurnside (1996) estimates returns o scale to bejust under1. Thereforewe set a,i + ak = 0.95,a value that does not departsubstantially romthe standardCRS assumption.Since the laborshare of income has averagedabout 0.65 overthe postwarperiod,we set a, = 0.65, implyinga value of ak = 0.3.The stochasticprocess for the level of tech-nology for incumbents is assumed to be de-scribedby the relation(26) z' pz + ,where s is assumed to follow a (truncated)normaldistributionwith 0 mean,standarddevi-ation of a- and finite support [-4a, 4of]. Theinitial level of technology for entrantsis as-

sumed to follow a uniform distribution overZ = [ - 4 f1 -p, 4o-Il -p].4The parametersp and o-have implications orthe degree of persistence and dispersion in thesize distributionof firms. We thus restricttheirvalues so that the model is able to (approxi-mately) replicate the second moments of thedistribution of investment rates, as obtainedfrom Compustat (Standard& Poor's, 1999a).5In our benchmarkmodel this implies choosingvalues of p = 0.62 and o- = 0.15.Similarly,the rate of depreciation n the cap-ital stock is set to equal 0.12 so that the modelmatchesthe average investment to capital ratiofound in the data.Finally, we are left with the fixed cost ofproductionf. Given the degree of returns toscale, the nature of the financing costs and thestructure or the idiosyncratic shocks, the fixedcost is closely connected to the level of firmturnover in the model. This is an importantelement in the analysis as we want to addressthe potential selection bias issues raised by thefact that the Compustat data set is itself anunbalancedpanel with significant irm turnover.We will quantify to matchthis fact closely ineach simulation.Financing Costs.-Modeling the costs of ex-ternal finance is a somewhat more complicatedissue and requiressome caution.Financialmod-els usually focus on two types of costs associ-ated with this activity: informationalcosts andtransaction osts. Informational osts are relatedto the extrapremium hat is associated with thebad signal thata firmmay transmit o the marketwhen tryingto raise funds as well as the dete-rioration n balance sheet. These costs are veryhard to quantify and the number of empiricalstudies that address the issue is very limited.Transactioncosts are generallyassociated withthe compensationto intermediariesplus all thelegal, accounting,and other bureaucratic osts.Constructingquantifiedmeasures of these costshave been the subjectof much research. Giventhe availabilityof data we will focus solely ontransactioncosts as a source of imperfection nfinancial markets.Clifford W. Smith, Jr. (1977) provides de-

3 The parameterA is introducedonly to scale the capitalstock. In each simulationwe recalibrateA so that the cross-sectional average of the capital stock is identical to that inthe data.

4 These conditions are imposed to satisfy Assumption 2.5 For a descriptionof the data see the Appendix.


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 127318 -16 -14-12-u 10 0

i6 - s'4 - .. .... .. .2 -0

0.75 2 3.5 7.5 15 35 75 300AmountRaised

FIGURE . COSTSOF ISSUINGSECURITIESNote: The top line signifies underwriting; he middle linesignifiesrightswith standby; hebottom ine signifiesrights.

tailed evidence on the flotation costs associ-ated with issuing new equity. His data coversall equity issues registered between 1971 and1975. Figure 4 is based on his work anddepicts these costs, as a fraction of theamount raised, for the different methods offinance. Regardless of the method used, thesignificance of economies of scale in thisprocess is clear: external funding can be ex-tremely expensive for very small operationsand this is reflected in the declining averagecosts of financing.To obtain a quantitativemeasure of thesecosts we fit a linear cost functionof the type(27) A = Ao+ A1X NewIssuesto this data and obtainthe following resultsforthe total costs of raising new equity (units inmillions of U.S. dollars):(28) A = 0.48 + 0.028 X NewIssues.

Since this regressionfits the data quite well(this should be expected given the patternofaveragecosts depictedon Figure4) we chooseto specify this functionalform for the unit costfunction and use our regression results to setA1= 0.028. Since the intercept erm is sensitiveto the unit of measurement, bettermeasure orAO an be obtainedby looking at the averagecost for very small issues. These averageabout0.108, implyingan intercept ermof Ao= 0.08,a value that we adopt. We will examine the

TABLE 1-CALIBRATIONBenchmarkParameter value Emiipiricalestriction

Technologyak 0.3 Degree of returns o scalea, 0.65 Laborshare8 0.145 Investment to capitalratioTechnology Shockp 0.762 Persistencein investmentr' 0.0352 Cross-sectionvariance ofinvestmentFinancing CostsAO 0.08 Fixed flotation costsAl 0.028 Unit flotationcostsPreferencesf 1/1.065 InterestrateH 0.6 Employmentshare

k

Unconstrained/\ / C~~~~~~~~~~onstraiiied

Exit

ExternalFinance

zFIGURE 5. FIRMBEHAVIOR

consequences of adopting alternativeassump-tions on the natureand the magnitudeof thesecosts later.Table 1 summarizesour benchmarkcalibra-tion procedure.B. Results

OptimalFirm Decisions.-Before character-izing the equilibrium and the full cross-sec-tionaldistributionof firmsin this economy, it ishelpful to develop some intuitionaboutoptimalfirm behavior.Figure5 providesa very simplequalitative llustrationof the combinedfinance-investment decisions. This representationhigh-lights a few of the interestingfeatures of thiseconomy. First, only firms with relatively lowlevels of productivity eave the market in anygiven period.Second,externalfinancing s usedonly by those firms who are eithervery smallor


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1274 THEAMERICANECONOMICREVIEW DECEMBER2001TABLE 2-AGGREGATE RESULTS

Variable ModelInvestmentshare(IIY) 0.21Share of financing costs (A/Y) 0.0062External inance/totalcosts 0.17Flotation costs/external finance 0.39

very productive (the "borrowing" irms). Theexplanation is simple: in the absence of fric-tions, productivefirmswould invest, anticipat-ing future levels of high productivity. Themarginal product of capital must be very high,or alternatively, they must be very far awayfrom their desired capital stock. In this case itpays to take the extra costs of raising externalfinance and invest.For firms either somewhat larger or some-what less productive, the difference betweenthe actual and desired level is not quite aslarge (or the marginal productivity of capitalis not quite as high), and it is not profitabletoaccept the financing costs. Since their invest-ment decision is constrained by the fact thatthey face costly access to external funds, wedefine these firms as "constrained." The re-maining firms are defined as "unconstrained"in the sense that they invest less than theiravailable funds. Notice that we actually ob-serve which firms are constrained by currentcash flows, unlike much of the empiricalliterature.

Aggregate Quantities.-Table 2 providessome summary statistics about the aggregatequantities generated by the stationary equilib-rium of the model. These are reasonably con-sistent with U.S. data with one exception: themodel implies that the financing costs areonly a very small fraction of total GDP. Thisis, of course, a consequence of the stylized,and limited, role of the financial sector and isnot altogether surprising.Table 2 also showsthe fraction of investment that is financed byexternal funds. The fact that these funds arevery expensive produces two effects: (i) adirect "cost"effect; firmsuse external financeinfrequently (about once in every sevenyears); and (ii) an indirect "size" effect; ifexternal funds are required, they are raised invery large quantities.

TABLE 3-CROSS-SECTIONAL RESULTS

Variable Data ModelMatched quantities

Average size (capital) 80.89 80.89InvestmentrateIIK 0.145 0.145StandarddeviationIIK 0.139 0.160Autocorrelation IK 0.239 0.191OtherquantitiesMean q 1.56 1.12Growthrate (sales) 0.036 0.031Average CFIK 0.292 0.221Standarddeviation CFIK 0.214 0.091Negative investment(fraction) 0.08 0.13Note: CF denotes cash flow

Firm Behavior.-Table 3 focuses on the mi-croeconomic implicationsof the model by ex-amining some summary statistics from thecross-sectional distributionof firms. The firstpartof the table containsthose variables hatthemodelwas calibrated o approximatelymatch nthe numericalexercise. Unfortunately, he highdegreeof nonlinearities n the solution makes itnearly impossible to match these moments ex-actly. Neverthelesswe see thatour approxima-tion appears quite reasonable along thosedimensions.The second half of the table concerns themodel's abilityto replicateother nteresting ea-tures of the data and thus provides a moreinterestingmeasure of the empiricalsuccess ofthe model. Consistentwith the early findingsofEric B. Lindenbergand Ross (1981), as well asseveral other more recent studies, we find thatthe model implies average values of q consis-tently above 1 on average. Here this is a con-sequence of industry selection: the survivingfirms in the sampleare the most profitableones.In addition,the model does a reasonably goodjob of replicatingsome features regardingthebehaviorof cash flow. Given the role thatq andcash flow play in the investment regressionsbelow, this is an important inding.

The Role of FinancingConstraints.-Table 4examines the role of financial constraints.It iseasy to see thatthey areclearlynontrivial n thebenchmarkeconomy: over half of all the firmsare constrained according to our definitionabove. Although these firms are somewhatsmallerthan the averageunconstrained irm, itappearsthat the significance of financingcon-


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 1275TABLE 4-FINANCE

Variable External inance Constrained UnconstrainedFirms 0.07 0.63 0.30Share of investment 0.79 0.74 -0.53Size (capital) 55.96 171.93 298.57Mean IIK 1.20 0.188 -0.086Tobin's q 1.34 1.14 1.08Marginal productof capital 0.24 0.22 0.19

straints s essentially determinedby the individ-ual productivity z) and not the size of the firm(k). This becomes clear from examining thenext rows: constrained irms have a highermar-ginal productivity of capital and invest morethan those unconstrained.They also have ahighervalue of Tobin's q on average.Marginal productivities provide an addi-tional insight into the model. The marginalproductivityof capital for constrainedfirms isactually higher than the rentalprice of capital(r + 6 = 0.21), thus they do not satisfy astandardEuler equation. Unconstrained firmson the other hand arerelatively unproductive.On average, however, they do not satisfy theEuler equation either: they overaccumulatecapital, as evidenced by the low marginalproduct.6'7A third group is made by thosefirms who use external finance. These areclearly the most productive of firms as theymust incur the financing costs. They are alsothe smallest on average.A potential problemwith the analysis aboveis that, n practice,we can not determineexactlywhich firmsarefinanciallyconstrained.A com-mon empirical proxy for this is firm size. Weexamine the results of applyingthis procedureto our model in Table 5. We separatefirms intwo categories: "small" firms, with a capitalstock below the sample average, and "large"firms, those whose size is above the marketaverage.

TABLE 5-FINANCE AND SIZE

Variable Small firms Large firmsFraction of firms 0.72 0.28Share of investment 0.85 0.15Size (capital) 139.80 359.79Mean IIK 0.185 0.035Fractionconstrained 0.61 0.39Exit rate 0.12 0.01Tobin's q 1.12 1.15Marginalproductof capital 0.21 0.22

An interesting feature of this model is itsability to replicatethe negative correlationbe-tween firm size and firm growth, extensivelydocumented by many authors (for example,David S. Evans, 1987; Bronwyn H. Hall, 1987).Small firms are growingfaster as evidenced bythe larger nvestment o capitalratio. Rememberthatin ourmodel, size dependson profitability:firms become large only because they had avery good history of technology shocks. Be-cause technology levels aremeanreverting heymust, at least on average, grow at a slower ratethan small firms.Small firmson the otherhandappearmore risky with very large annual exitrates.Despitethe fact that more smallfirmsfacefinancing constraints,the size of the firm ap-pearsas a very imperfectproxyfor the existenceof financingconstraints.There are two reasonsfor this: (i) the persistencein the idiosyncraticshocks renders productivity largely uncorre-lated with size and,as we have seen above, (ii)several small firms are actually using externalfunds,and thus are not financiallyconstrained.86 This subgroup ncludes a large fraction of the exitingfirms which explains the large averagedrop n investment nthis sample.7This result however is not robust. Here capitalaccumulation is the only way firms can insure againstpaying financing costs in the future. Relaxing this as-sumption, however, does not change our main results

about the absence of cash-flow effects. Results for aversion of the model with cash holdingsare availableuponrequest.8 This fact is also documentedby some Euler-equation-based tests of financingconstraints(see Whited, 1992, forexample).


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1276 THEAMERICANECONOMICREVIEW DECEMBER2001IV. Empirical ImplicationsA. InvestmentEquations

The equilibriumdistributiongeneratedby thesolution to the model is suitable to address theissue of estimating reduced-form investmentequations.Section I noted the emphasis placedby several studies on these econometric proce-dures to determine he relevance of finance con-straints. The empirical methodology is tospecify a functional form for investment of thetype(29) k = bo + blqi,t- I

+ b2 7Ti'ti +ft + di + 6i,ti,t - 1where

(30) qi,t =ikpi,tandp is the marketvalue of the firmdefinedin(6). Hence we are using beginning of periodaverage q andbeginningof periodcash flow inthese regressions; ft is a year effect and didenotes a firm-specific fixed effect. The yeareffects are introduced o eliminate the effects ofbusiness cycles in the regression.

EmpiricalResults.-The basic source for ourempiricalanalysis s the Compustatdataset. Weuse the combined annual, full coverage, andresearch1998 files. We startoursamplein 1979since the coverage of over-the-counter firmsincreasedsubstantiallyafter this year, giving usa much largercross section of firms.Substantial hangesin reportingand account-ing methods lead us to stop the samplein 1988(for details, see Ben S. Bernanke et al., 1990).The total number of firms in this sample forthese years is 9,761. This numberis then sub-stantially reduced to eliminate the effects ofunreliable data, outliers, and events such asmergers, in the sample period described. Af-ter these procedures are applied we are leftwith an unbalancedpanel of 12,321 firm-yearobservations.The second column of Tables 6 and 7 docu-

TABLE 6-STANDARD INVESTMENT EQUATIONS

Benchmark No financingCoefficient Data model constraintsb, 0.06 2.82 8.07(0.01) (0.08) (0.10)R2 0.12 0.53 0.84Note: Standard rrors are in parentheses.

TABLE 7-CASH-FLOW-AUGMENTED EQUATIONSBenchmark No financingCoefficient Data model constraints

b, 0.06 4.13 11.52(0.01) (0.39) (0.05)b2 0.14 -2.67 -10.19(0.04) (0.77) (0. 10)R2 0.25 0.53 0.98Note: Standard rrorsare in parentheses.

ments the resultsof estimating equation (29) infirst differences with and without imposingb2 = 0 9As others before us we also find a "cash-floweffect": the cash-flowregressorappears o sub-stantially improve the predictive power of theregression as the adjusted R2 also improvessubstantiallywhen this variable is included.

Theoretical Results.-We now turn to theresults of estimating equation (29) using theartificial data generated by our model. Tomake these results comparable we simulateall of our economies below over a period often years using the transition function (13).We then scale the stationary distribution offirms (12) (which is a measure) so that wehave, in every period, the average numberoffirms in the Compustat sample (a little over1,200). This will then be our artificial coun-terpart to the Compustat data set. We thenapply the same econometric procedures toestimate (29) for this data.10Finally we repeatthis procedure 1,000 times and report thesample means for both coefficients, the stan-dard errors, and the adjustedR2.9This procedure is commonly employed as possiblecorrection of measurementerror n several studies.10Year effects arenot necessary since we are only look-ing at a nonfluctuating conomy. Nevertheless this is veri-fied for the artificialdata.


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 1277The results for our benchmark model areshown in the thirdcolumn of Tables 6 and 7.We obtain threeconclusions from this exercise.First, relative to the standardneoclassicalmodelwe find that ourbenchmarkcalibrationdeliversa muchlower correlationbetween q andinvest-ment. This is not very surprisinggiven thatwehave departedsubstantially rom the strongho-mogeneity assumptions often imposed in theliterature.As a result, the propercharacteliza-tion of the investmentdecision of each firmwillnot, in general,resemble a simple linear func-tion of averageq. Given theempirical ailure ofsimple q models, this is probablya good result.Second,thecoefficienton q is muchhigherthan

in the data. This result was also documentedbySargent's (1980) early study and shouldnot bevery surprisingas the optimalinvestment deci-sions in this model follow some type of (s, S)behavior and involve some dramatic, althoughinfrequent,changesin investmentrates at sometrigger points. It is well known that one caneasily eliminate this problem by introducingsome additional convex adjustmentcosts oninvestment. Since our goal is to understand he"cash-flow effect" and not to replicateindivid-ual coefficientswe abstract rom these for sim-plicity. Third,and more importantly,we do notfind evidence of a cash-flow effect. Unlike ourempirical results, the cash-flow-augmentedre-gressions add no significant explanatorypowerto the investmentequation. Although financialconstraints are very important or many firms,as we have seen in Table 4, the independentinformational ontent of cash flow appearsquitesmall.11The last column is the most convincing: itshows the results of estimating(29) for a modelwith nofinancing constraintsat all. Thatis, forthismodelwe have set the functionA() equalto

zero everywhere.Here however we do find acash-flow effect. The implication of these re-sults is quite apparent:not only is the existenceof financialconstraints not sufficient to estab-lish cash flow as a significantregressorbeyondaverage q, but it also appearsnot to be neces-sary. This is animportant esult. It is natural hatwe may ask whether it survives alterations nour benchmarkmodel.Alternative Samples.-To better understandour results it is instructive, however, to firstreplicate regression (29) for altemative sub-samples of firms. In paiticular we considersix common types of subsamples: "balanced

panel" of firms, "small" versus "large" firms,and"constrained,""unconstrained,"and "bor-rowing" (those who use external funds) firms.Clearly several of these subsets overlap. Weemphasize again that the exact identi-fication of "constrained," "unconstrained,"and "borrowing" irms is only possible in themodel.Tables 8 and 9 illustratetwo main results.12First, we find no evidence of strong cash-floweffects, with the possible exception of the "un-constrained"and "small" samples. The resultfor unconstrainedfirms is very curious: cashflow is significant for firms who are clearlyidentified as not suffering from financial con-straint.Second, cash-flow effects do not existfor the subsampleof "constrained"irms.Againthis is a very strongresult. Takentogetherthesetwo results are again very suggestive of the(lack of) statisticalpowerof theseregressionsasa useful means of identifying financially con-strained irms.Why does cash flow add any explanatorypower at all in some of these regressions?Simply because of specification error: theright equation for investment behavior is thepolicy rule (8). For some firms this function ishighly nonlinear and a linear function of qdoes a very poor job. In this case cash flowmay improve the quality of the linear approx-imation. As we have seen, however, this hasnothing to do with financing constraints.

" This is true despite the large and highly significantcash-flow coefficients in the regression. There are at leastthree reasons for this. First, as we have noted above, sincewe abstracted rom convex adjustment osts in this model,the regression coefficients will be generally quite large.Second, as we will see below, with technology shocks cashflow becomes hlighlycorrelatedwith q. Third, the equationis badly misspecifieddue to the (generally)highlynonlinearnature of investment decisions. All these render the esti-matedcoefficients on these l inear equations ratheruninfor-mative. Instead we choose to focus on the adjustedR as abetter indicator of additional informative content of thecash-flow regressor.

12 Qualitatively, hese results are not always independentof model specification. Nevertheless, they survive most ofthe extensions and provide a clear example of theproblemsin interpreting he results of these regressions.


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1278 THEAMERICANECONOMICREVIEW DECEMBER2001TABLE 8-STANDARD INVESTMENT EQUATIONS: SUBSAMPLES

Coefficient Data Balanced panel Constrained Unconstrained External finance Large Smallb, 0.06 2.12 0.60 1.83 4.79 3.19 1.99(0.01) (0.78) (0.02) (0.14) (0.30) (0.07) (0.21)R2 0.12 0.58 0.99 0.34 0.98 0.74 0.71Note: Standard errors are in parentheses.

TABLE 9-CASH-FLOW-AUGMENTED EQUATIONS: SUBSAMPLES

Coefficient Data Balanced panel Constrained Unconstrained External finance Large Smallbi 0.06 8.09 0.04 15.59 12.01 6.15 18.60(0.01) (0.34) (0.12) (0.94) (0.45) (0.34) (2.20)b2 0.14 -12.57 1.13 -22.48 -17.13 -5.82 -37.60(0.04) (0.70) (0.24) (1.54) (1.00) (0.66) (4.98)R2 0.25 0.61 0.99 0.52 0.99 0.77 0.83Note: Standard errors are in parentheses.

B. Alternative SpecificationsWe now examine the robustnessof our find-ings by extending the benchmarkmodel alongseveral dimensions. Although the quantitativedetails change across different specifications,the strong qualitative message remains: infor-

mation about financing constraints should becapturedby the (appropriatelymeasured) q re-gressor and cash flow is essentially redundantand uninformative.Alternative Financing Constraints.-Thecalibration of the function A() that describesthe costs of raising externalfinance was basedon data about the transaction costs of issuingnew equity. There are a number of reasonswhy we may want to expand upon this initialcharacterization. First, from an economicviewpoint one may argue that equity financeaccounts for only a small fraction of totalexternal finance. A bank loan, say, may wellhave much lower costs than those we haveassumed above. Second, from a mathematicalperspective one may also be interested inexamining whether our results are sensitive tochanges in the functional form of A().In this section we consider two alternativespecifications of the financing costs functionA(). While these are not exhaustive they

cover some of the obvious extensions onewould like to examine and provide a verygood indication of the robustness of our initial

findings. In all experiments we adjust thecalibration of the technology shocks to stillmatch the investment distribution (the firstpart of Table 3) closely.Our first experiment is a nice blend of ourtwo considerations above. Motivated by therelatively low costs of bank finance that mostfirms use, we interpret A() as the differencebetween a "borrowing"rate (r + A), at whichexternal funds can be obtained from banks,and a "lending" rate (r), implicit in the op-portunitycost of internal funds to firms. For-mally we impose(31) A = 0.02 X Borrowing.

The interest rate spreadis then set at 2 per-cent, the average spread between six-monthCDs (lending rate)andthe primerate (borrow-ing rate) for the period 1968-1997.13An alternativeexperience is to focus on therole of the fixedcosts in thefunctionA(). To doso let(32) A = 0. 15.

13 An alternativewould be to use the rate of commercialpaper nstead of the prime rate.This would imply aninterestrate spreadof around0.5 percent. However, manyfirms donot have access to commercial paper. In addition,a modelwith such a small interest rate spread s very similarto themodel without financing constraintsdiscussed above.


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 1279TABLE 10-STANDARD INVESTMENTQUATIONS:

ALTERNATIVEPECIFICATIONSFinancing costs Marginal

Coefficient Data Variableonly Fixed only qb, 0.06 2.92 2.82 -0.86(0.01) (0.07) (0.11) (1.03)jR 0.12 0.61 0.32 0.06Note: Standard rrorsare in parentheses.

This specification s somewhatsimilarto thoseused in the investmentwith fixedcost literature.Note that the fixed cost is about 50 percenthigherthan in the initial calibration.The resultsof estimating quation29)for thesealternativemodelsare displayedn columns3 and4 of Tables 10 and 11. We find that the linearequations a poorer it when fixedcosts are veryhigh.Againthis is becausehigh fixed costs giverise to very discontinuousnvestmentdecisions.Eliminating he fixed costs, on the otherhand,improves he overallqualityof thefit. Regardless,the adjustedR2 still changesvery little with theinclusion of cash flow in the regressions.Againwe see no evidenceof a strongcash-floweffectinthe artificialdata.Marginalq.-The finalcolumnof Tables 10and 11 looks at the performanceof an alterna-tive specificationof equation 29) thatuses mar-ginal, instead of average, q as a measure offundamentalsor the benchmarkmodel. We de-fine marginalq as the right-handderivativeofthe value functionp(k, z).

(33) Lim p(k +h z) -p(k, z)h- o+ hWe find that, as first documented by Cabal-lero and John V. Leahy (1996), average q canactuallyperformmuch betterthan marginalq inthese reduced-formequations.This is a conse-quence of the discontinuityin the investmentdecision of the firm in the presence of fixedcosts. Caballeroand Leahy (1996) show thatinthis case, investment is not even a monotonicfunction of marginalq. In the context of ourbenchmark alibrationwe findthatit is actually

possible to obtain an overall negative correla-tion between the two variables.The weak performanceof marginal q ex-

TABLE 1 1-CASH-FLOW-AUGMENTED EQUATIONS:ALTERNATIVE SPECIFICATIONS

Financing costs MarginalCoefficient Data Variable only Fixed only qb 1 0.06 4.88 6.25 -0.22(0.01) (0.29) (0.50) (0.45)b2 0.14 -4.11 -7.00 5.41(0.04) (0.59) (1.00) (0.16)R2 0.25 0.63 0.35 0.50Note: Standard errors are in parentheses.

plains the success of cash flow in this regres-sion. Again, however, we arguethat this is soonly because we have a very poor measureoffundamentals.

C. ProductivityShocks, Cash Flow,and InvestmentThe robustness of the previous results isstriking. Despite the importantrole of financ-ing constraints in the investment decision ofthe firm we find that the cash-flow regressoris, in general, only marginally significant.Perhaps even more surprising, we find thateven when cash flow has a strong role in theaugmented investment equations, this givesvery little information on the importance offinance constraints.Tables 12 and 13 provideus with some of theintuition behind these results. They depict thecross correlationsbetween the variables of in-terest for our full sample of firms,for both thesimple benchmark model and the versionwithout any financing constraints.14 In bothcases it is apparent the strong collinearity

between q, cash flow, and also sales, herejustequal to output. Moreover all of these vari-ables are also strongly correlated with thetechnology shock as well. As Sargent (1980)pointed out, this is importantbecause in thecontext of a fully specified general-equilib-rium model with productivityshocks the stan-dard investment regressions are generally notjustified on theoretical grounds as both the14 With the exception of cross correlationswith invest-

ment, which are usually a little higher, the results arequantitativelyvery similarfor the other subsamples hat wehave studied.


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1280 THEAMERICANECONOMICREVIEW DECEMBER2001TABLE12-CROSS CORRELATIONS: TABLE 13-CROSS CORRELATIONS:BENCHMARK ODEL No FINANCING ONSTRAINTS

Tobin's Cash Tobin's CashVariable Investment q flow Sales exp(z) Variable Investment q flow Sales exp(z)Investment 1.00 0.53 0.57 0.56 0.53 Investment 1.00 0.45 0.45 0.48 0.42Tobin's q 1.00 0.92 0.93 0.92 Tobin's q 1.00 0.95 0.97 0.95Cash flow 1.00 0.99 0.96 Cash flow 1.00 0.99 0.98Sales 1.00 0.95 Sales 1.00 0.97exp(z) 1.00 exp(z) 1.00

right- and left-hand-side variables are endog-enous. Indeed previous work by Shapiro(1986) shows how, by ignoring the effect ofthe underlying exogenous shocks, we cangenerally expect to obtain a spurious correla-tion between investment and output (or cashflow) that can not be interpreted as evidencefor an accelerator type model or, in our con-text, as evidence of financing constraints. Asa result, estimation of a reduced-form equa-tion like (29) is clearly inappropriate,not onlybecause it does not describe the correct deci-sion rule of the firm (6), but also because itwill, in general, be unable to incorporate theeffects of the technology shock, z, on theendogenous variables.As a related point Tables 12 and 13 alsosuggest that, since all variables are stronglycorrelatedamongst themselves, one can expectthat measurementerror n one of them (q, forexample) may lead an econometrician o assigna largerrole for the others(cash flow and salesusually) in the regression. As our exercisesdemonstratehowever, this is, essentially, with-out economic significance.

D. MeasurementErrorThe resultsabove areimportantn two ways.First, they make it clear that the existence offinancialconstraints s not sufficientto establishcash flow as a significant regressor, beyond q.In the context of a fully specified model, theeffect of financial constraintsmust be alreadyincluded in the market value of the firm andshould also be capturedby q. Second, the col-linearity between cash flow and q suggests thatany sizable measurementerror n the construc-

tion of q can reduce the overall correlationbetweenq and investmentandperhapsgeneratea cash-flow effect.

In this section we explore these ideas byanalyzing the effects of measurement erroronour theoretical regressions. First, we explorethe effects of measurement error in the stockof capital, certainly one of the variables thatrequires more assumptions in its empiricalconstruction. A simple way to illustrate thispoint is to make the price of capital goodsunobservable to the econometrician. Thismeasurement error in the construction of thecapital stock is only one of several identifiedby researchers n empiricalstudies.To consider this we provide yet another ex-tension of the benchmarkmodel with stochasticprices for investment goods. Specifically weassume that investment goods can be trans-formed into consumption goods at the relativeprice4. This rateof transformations stochasticand firm specific, reflecting diosyncratic hocksto the value of the firm's capital stock. Theshock to the value of investment goods wascalibratedusing data from JeremyGreenwoodet al. (1997) on thebehaviorof the relativepriceof investment goods. They estimate that the(detrended)price of investment goods followsthe process(34) )' = 4(1 - 0.64)

+ 0.644 + 6, o = 0.035,where 4, the average value of capital goods inunits of consumptiongoods, is normalized o 1.We assume thatthese values hold for ourmodelas well and restrictthe distributionof the inno-vations to be normal for incumbentsand uni-form for new entrants. While this calibrationprocedure s not theoreticallycorrect it is nev-ertheless used to providea simpleillustrationofthe effects of measurement error in cross-sectional investmentregressions.


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VOL. 91 NO. 5 GOMES:FINANCING NVESTMENT 1281TABLE 14--STANDARD INVESTMENT EQUATIONS: MEASUREMENT ERROR

Measurement error Measurement error Measurement errorCoefficient Data Capital stock Classical No constraintsb,10.06 2.08 1.59 6.71(0.01) (0.24) (0.08) (0.12)R2 0.12 0.29 0.18 0.73Note: Standard errors are in parentheses.

TABLE 15-CASH-FLOW-AUGMENTED EQUATIONS: MEASUREMENT ERROR

Measurement error Measurement error Measurement errorCoefficient Data Capital stock Classical No constraintsb, 0.06 0.65 0.45 8.19(0.01) (0.61) (0.09) (0.14)b2 0.14 1.25 4.72 -5.35(0.04) (0.40) (0.22) (0.32)R2 0.25 0.39 0.46 0.81Note: Standard errors are in parentheses.

To introducemeasurement rror n the capitalstock we assume that the econometriciancannot observe the actual price of the investmentgoods, 0, and simply estimates this to be con-stant across firms and equal to its average valueof 1.The results of this procedureare documentedin the thirdcolumnof Tables 14 and 15. Whileall correlationsarenow lower, we observe thatcash flow does increase the overall explanatorypower of the regression. While the improve-ment is not dramatichere it illustrates the po-tential of the measurement-error rgument.Inthis case the success of the cash-flow regressoris clearly identified from our theoreticalcon-struction.It is only due to the problemsassoci-ated with the constructionof the q variable thatwe obtain significantcash-flow effects.A moredirectalternatives perhaps o exam-ine the effects of introducingclassical measure-ment error n averageq. As a simple illustrationsupposethatthere is some normallydistributednoise that prevents the econometrician fromhaving an exact measureof average q. Specif-ically, supposethattheeconometricianobservesonly(35) q-=q + (,(~ N(O, 0-).

We thenset o2 equalto ?loof the varianceofq, implying a signal to noise ratio at 10. This

may or may not be conservative but again thiscalculation is intended as merely suggestive.The results in column 4 are those one wouldexpect with classic measurementerror: lowercoefficients on q and lower R2 as well. Inter-estingly the cash-flow effect also seems strongerin this case.Finally we also show the results of introduc-ing classic measurementerror for the modelwithoutfinancingconstraints.Again these con-firm thatfinancingconstraintsarenot necessaryto observe cash-flow effects, in the sense thatthe adjustedR2 increasessignificantly.The conclusion from these experiencesseems, by now, quite clear: regardless of themodel the existence of financial constraints sneithersufficient nor necessaryto establish cashflow as a significantregressor, beyond q. Thecash-floweffects areeithera combinationof theartificialcorrelation nducedby the technologyshocks and the measurementerror in q or aconsequenceof the nonlinearities n investmentand the poor fit of (29).

V. ConclusionsMacroeconomists often emphasize the roleof financial constraintsas an importantsource

of propagation of shocks across time andfirms. Moreover, recent work by Bernankeand Alan S. Blinder (1988), Anil K Kashyap


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1282 THEAMERICANECONOMICREVIEW DECEMBER2001et al. (1993), Bernanke et al. (1997), andThomas F. Cooley andVicenzoQuadrini 1998)suggests that n the presenceof these constraints,monetarypolicy can have powerful effects onindividual firm decisions and aggregate condi-tions. Much of the evidenceon therole of financ-ing constraintst thefirm evel relies on the resultsof estimating cash-flow-augmented nvestmentequationslike (29).This workquestions he conclusion hatone cansafely attributehe empirical uccess of cash flowto the importance f financingconstraintsn in-vestmentdecisionsby firms.Wedo so by address-ing this issue from a different,more structural,perspective.We begin by fully specifyinga modelof investmentunder financialconstraints onsis-tentwithseveralempirical egularities bout irmbehaviorobserved n the data.We obtain three main findingsfrom this ar-tificial panelof firms.First, despitethepresenceof liquidity constraints,it is hard to find evi-dence that cash flow adds significant explana-tory power to the investmentregressions.Thusthe existence of financial frictions is not suffi-cient to obtainsignificantcash-flow effects. Weargue that, in the context of a fully specifiedmodel, the effect of financialconstraints houldbe includedin the marketvalue of the firmandthuscapturedby a good measureof q. Second,financingconstraintsare also not necessary toobtain these cash-flow effects in the model. It ispossible to construct simple examples wherecash flow adds some predictivepowerto invest-mentequations,even in the absenceof financialfrictions.Third,as Sargent (1980) and Shapiro(1986) documented,we findthat,in the contextof these general-equilibriummodels, the corre-lationbetweeninvestment,cash flow, and salesis quite artificial and a reflection of the under-lying technology shocks. Clearly this impliesthat the focus on reduced-form investmentequationscan be quite problematic. n a relatedpoint, we also find that it is also possible toobserve cash-floweffects solely due to the mis-specification nducedby fittinga linearequationto a nonlineardecision rule.These results suggest that the presence ofmeasurement error in one of these variablesmay lead an econometricianto assign a largerrole to others.We formallyconfirmthis conjec-tureby explicitly examiningthe effects of mea-surementerror n investmentregressions.These findings, however, do not questionthe

existence or the importanceof these constraintsfor investmentdecisions and/or he propagationof monetarypolicy shocks. It may well be thatthese constraintsare relevant n practice.Infact,this approach to modeling equilibriuminvest-ment and financingbehavior,can be extendedtoaccount for aggregatebusinesscycles andmon-etary policy shocks thusprovidingan ideal lab-oratory o study the importanceof these effects.Nevertheless our results highlight the enor-mousdifficultiesn usingstandardnvestment e-gressionsnpractice,andcast seriousdoubtonthecommon nterpretationf cash-floweffects as ev-idencein favor of financingconstraints.APPENDIX

This Appendix provides a brief descriptionof the sources and methods used to generatethe stylized facts analyzed in the text.15A. Variables

Investment.-Investment expenditures, it' isspendingon plant,property,andequipmentmi-nus capitalretirements.CapitalStock.-We use the perpetual nven-tory method described in Michael A. Salingerand Summers(1983) to convert the book valueof the gross capital stock into its replacementvalue:

(Al) Kit = [Ki -1( pk) + Ii,t (1 -2ILt),where the recursion s startedwith the reportedvalue of the capital stock in the first year thefirm is in the Compustatfiles, pk denotes theprice of capital goods, taken to be the deflatorfor nonresidentialfixed investment from DRI(Standard& Poor's, 1999b), andLt is the aver-age life of capital goods computed using thedouble declining balance method as(A2) it DEP,

15 See Whited (1992) for a more detailed description.


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VOL.91 NO. 5 GOMES:FINANCING NVESTMENT 1283with K' denotingthe reportedvalue of the cap-ital stock at period t.

MarketValue.-Market value of a firm,Vi,tis constructedas(A3) Vit = Di,t + Eit - INVit,where Ei,t is the market value of equity, Dt isthe value of short- plus long-term debt, andINVt is the end-of-periodvalue of inventories.The marketvalue of equity is the sum of com-mon equity (numberof sharesoutstanding imesthe end-of-periodmarket price) plus preferredequity (firmpreferredpay-outdividedby S&P'spreferreddividendyield, from theDRI dataset).

Average Q.-Tobin's q (beginning of pe-riod) is computed as

(A4) Qi-t KKi,t- ICash Flow.-Cash flow is definedas the sumof operatingincome and depreciationfor theperiod.

B. SampleSelectionMost previousstudies documenta numberofirregularities in the sample period described,such as mergers,reporting,and/orcodingerrorsetc.'6 To maintaincomparabilitywith the exist-ing literaturewe use the following procedure oeliminate extreme observations:

* The capital stock must be positive in allperiods;* Investment can not exceed beginning of pe-riod capitalstock;* Tobin's q must be positive and can not ex-ceed ten;* Cash flow (in absolutevalue) can not exceedfive times the capital stock;* The capital accumulationequation must besatisfied.

16 Gilchrist and Himmelberg (1995), Abel and Eberly(1996), and Cummins et al. (1998), for example.

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