financing investment - penn: university of pennsylvania

Financing Investment

By JOAO F. GOMES*

We examine investment behavior when firms face costs in the access to externalfunds. We find that despite the existence of liquidity constraints, standard investmentregressions predict that cash flow is an important determinant of investment only ifone ignores q. Conversely, we also obtain significant cash flow effects even in theabsence of financial frictions. These findings provide support to the argument thatthe success of cash-flow-augmented investment regressions is probably due to acombination of measurement error in q and identification problems.(JELE22, E44,G31)

A recurrent puzzle in the investment litera-ture is that measures of Tobin’sq and of thecost of capital appear to have a negligible im-pact on investment. A recent strand of 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 that financial constraints play an impor-tant role in shaping corporate investment: (i)cash flow is highly significant in investmentregressions; and (ii) small firms appear moreliquidity constrained than large ones. These mi-cro data sets have also allowed researchers touncover a wealth of new empirical regularitiesabout firms and their investment decisions: (i)investment is lumpy, periods of low investmentare followed by large investment spikes; (ii)small firms grow faster and invest more thanlarge firms; and (iii) entry and exit rates are verylarge.

We seek to understand these facts using amodel of investment behavior where heteroge-neous firms face costly external finance. In thisenvironment firms seek to maximize their valueby making three interrelated decisions: (i) theymust choose whether to participate or not in the

market; if they decide to participate they 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 constraints andtheir implications for the performance of empir-ical investment equations.

Using the model’s stationary distribution offirms to run standard investment regressions, weobtain four main findings. First, the existence offinancial constraints is not sufficient to establishcash flow as a significant regressor in standardinvestment equations, beyondq. In the contextof a fully specified model, the effect of financialconstraints should be already included in themarket value of the firm and thus should also becaptured byq. Second, financing constraints arealso not necessary to obtain significant cash-flow effects. We show that it is possible toconstruct examples where cash flow adds somepredictive power to investment equations, evenin the absence of financial frictions. Third,as Thomas J. Sargent (1980) and Matthew D.Shapiro (1986) documented, we find that, in thecontext of these general-equilibrium models, aspurious correlation between investment, cashflow, and output is likely if one neglects theeffects of underlying shocks. Clearly this im-plies that focusing on these reduced-forminvestment equations is quite problematic. Fi-nally, we study the effects of alternative sourcesof measurement error in the model. As ex-pected, we find that using incorrect measures offundamentals can lead an econometrician to 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]). I would like to thankAndy Abel, Rui Albuquerque, Marty Eichenbaum, Fran-cisco Gomes, Jeremy Greenwood, George Hall, HugoHopenhayn, Per Krusell, Sergio Rebelo, Richard Rogerson,Amir Yaron, two anonymous referees, as well as numerousseminar participants for all the valuable comments. Finan-cial support from JNICT and the Bank of Portugal is grate-fully acknowledged. Any errors are mine.

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findings highlight the enormous difficulties inusing standard investment regressions in prac-tice, and they cast serious doubt on the commoninterpretation of cash-flow effects in the data asevidence of financing constraints.

This paper is organized as follows. Section Iprovides a brief overview of recent empiricalfindings about investment behavior and its rela-tion to financial variables. Section II describesour economic environment. Section III detailsboth the calibration methods and characterizesthe competitive equilibrium generated by themodel. The theoretical implications for the em-pirical investment equations are then examinedin Section IV. Section V summarizes ourfindings.

I. Investment and Finance

A. Investment Behavior

Investment is a central macroeconomic vari-able. Its fluctuations account for a large frac-tion of the cyclical volatility of output and in-come, and most economists link high rates ofinvestment to long-run economic growth. Un-fortunately, understanding investment behaviorhas proved to be a very difficult task (seeAndrew B. Abel, 1980; Abel and Olivier J.Blanchard, 1986). Earlier work focused on rep-resentative agent frameworks with convex coststhat smooth investment over time (Dale W.Jorgenson, 1963; James Tobin, 1969; Robert E.Lucas, Jr. and Edward C. Prescott, 1971; FumioHayashi, 1982, among others). Empirical workbuilt 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 short period oftime, while most periods are characterized byonly minor changes to the existing capital

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 theorems no longer hold. The largenonlinearities in investment behavior imply thatthe cross-sectional distribution of firm/plant-level investment may affect aggregate variables,which requires modeling firm heterogeneityexplicitly (Ricardo J. Caballero and EduardoEngel, 1994; Caballero et al., 1995; Abel andEberly, 1996; Marcelo Veracierto, 1997; Rus-sell Cooper et al., 1999).

B. Finance

In contrast with the predictions of the FrancoModigliani and Merton H. Miller (1958) theo-rem, most firms seem to prefer internal sourcesto finance investment. According to Stephen A.Ross et al. (1993), about 80 percent of all fi-nancing is done with internally generated funds.Explanations for this behavior usually highlightthe role of information asymmetries (Stewart C.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, Stephen M. Fazzari et al.(1988) find that low-dividend-paying firms (apriori more likely to be financially constrained)are generally smaller, invest more, and grow

FIGURE 1. FIRM-LEVEL INVESTMENT SHARES

1264 THE AMERICAN ECONOMIC REVIEW DECEMBER 2001

faster than high-dividend firms. They also havehigher cash flows and higher averageq’s.

In addition, reduced-form investment equa-tions find evidence of highly significant cash-flow effects while, on the other hand, Tobin’sqappears to have only a marginal impact on in-vestment. A number of authors have interpretedthis as evidence supporting the existence ofsignificant finance constraints, particularly forsmall firms.

Several other studies cast doubt on this inter-pretation however. From a theoretical stand-point, work by Sargent (1980), Shapiro (1986),and, in a somewhat different context, Peter M.Garber and Robert G. King (1983), suggest anumber of potential problems with the estima-tion of reduced-form equations from structuralmodels of firm and investment behavior. In par-ticular, they show that when the underlyingshocks to output and cash flow are positivelyautocorrelated it is possible to obtain strong, butquite spurious, correlations between these vari-ables and investment when one ignores morestructural information.

On the empirical side, work by SimonGilchrist and Charles P. Himmelberg (1995),Jason G. Cummins et al. (1998), and TimothyErickson 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’sq being used. Althoughtheir methodologies and results differ some-what, two common findings emerge.1 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 investment regressions is verydifficult to understand, however, due to the ab-sence of a solid theoretical structure behindthese reduced-form regressions. Our main goalhere is to provide a theoretical backgroundagainst which one can better understand theseresults.

II. Economic Environment

A pattern that emerges from the evidencediscussed is one of substantial firm heterogene-ity across a number of different characteristicssuch as firm size, growth, investment, and fi-nancing patterns. It seems, then, important thatour framework be consistent with this and thusable to produce a well-defined distribution offirms 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-straints at the firm level as in William A. Brockand Blake LeBaron (1990) and entry and exit inthe tradition of Boyan Jovanovic (1982) andHugo A. Hopenhayn (1992). Financial interme-diation is not modeled explicitly however. In-stead we proceed in the spirit of work by S. RaoAiyagari and Mark Gertler (1991) and JavierDiaz-Gimenez et al. (1992), and summarize thiscostly activity with a simple functional formthat captures the basic notion that external fundsseem to be more costly than internal ones. Thisis sufficient to make internal funds “valuable”for firms.

The economy consists of three sectors:households, financial intermediaries, and pro-ducers. Households are represented by a singleagent maximizing lifetime utility. Incomecomes from wages and dividends on the sharesthat the household holds in every firm. Firmsproduce a single output that can be transformedin either capital or consumption goods, combin-ing labor services with capital goods. Firms paydividends directly to the consumer but require

1 Briefly, Gilchrist and Himmelberg (1995) adopt a pro-cedure similar to that developed in Abel and Blanchard(1986) to construct an alternative measure of fundamentalsthat is then used in standard investment regressions insteadof averageq. Cummins et al. (1998) use earnings forecastsfrom the I/B/E/S data set to construct an alternative measureof fundamentals. This is then used in both the standardinvestment equations and also in some semiparametric re-gressions. Finally, Erickson and Whited (2000) develop avery sophisticated econometric methodology based on high-order Generalized Methods of Moments (GMM) estimators,specifically designed to handle measurement error. Minordifferences also exist in the definition of variables andsample construction.

1265VOL. 91 NO. 5 GOMES: FINANCING INVESTMENT

the services of financial intermediaries to obtainadditional funds. Financial intermediaries arealso summarized in a single agent that providesthese services at some cost.

A. Firm Behavior

Production is carried out 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 period there is also a continuum ofpotential entrants that decide whether or not toenter the market. Entrants choose to enter alsoat the beginning of the period before any currentvariables are observed.

Production requires two inputs: capital,k,and labor, l , and is subject to an individualtechnology shock,z. Firms hire labor at themarket wage ratew . 0 and discount futurecash flows by a factor ofb [ [0, 1). The spaceof inputs is a subset of the space of (nonnega-tive) real numbers,_ 3 + # 51

2 . The stochas-tic process for this shock has boundedsupportZ 5 [z, z], 2` , z , z , `. AlsodefineJz andJk as, respectively, the minimalsigma-fields generated byZ and_. Productionof the single good is carried out by each firm

according to the production functionF: _ 3 +3 Z 3 51. Assumption 1 summarizes theconditions imposed onF.

ASSUMPTION 1: The production function F:_ 3 + 3 Z 3 51 has the following proper-ties: (i ) strictly increasing, strictly concave,twice continuously differentiable, homoge-neous, and satisfies the Inada conditions;(ii )@h . 0, F(hk, hl, z) , hF(k, l , z).

Without decreasing returns to scale [part (ii)]the individual decision rules and the distributionof 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 thefirm remains in the market.

Assumption 2 below concerns the idio-syncratic technology shocks. We usez9 to de-note the value of next period level oftechnology.

ASSUMPTION 2: (a) Incumbents’ shocks(i )are uncorrelated across firms, and(ii ) have acommon stationary and monotone(increasing)Markov transition function Q( z9, z): Z 3Jz3 [0, 1] that satisfies the Feller property;(b)entrants draw their initial level of technology in-dependently from a common distributionw( z).

Without idiosyncratic shocks the productionsector could be consolidated into a single pro-ducer, as all firms would not only have the samedecision rules, but would also make the samechoices. For simplicity it is assumed that the sto-chastic process for each firm follows a commonMarkov process. Monotonicity of the transitionfunction guarantees that profits are increasing inthe current shock, a result that will prove usefullater. Assumption 2 also determines the distribu-tion of shocks for new firms. These are assumed tobe drawnafter the entry decision is made, poten-tially implying substantial heterogeneity in pro-ductivity across all new entrants, a fact consistentwith the evidence in Dunne (1994).

We can now summarize the static decisionsof the firm, thus simplifying the dynamic deci-sion problem below.

● Profits

(1) p~k, z; w! 5 maxl $ 0

$F~k, l ; z! 2 wl 2 f %.

FIGURE 2. TIMING OF EVENTS


● Labor Demand

(2)

l ~k, z; w!5 argmaxl $ 0

$F~k, l ; z!2 wl 2 f %.

● Supply of Output

(3) y~k, z; w! 5 F~k, l ~k, z; w!; z!.

Assumption 1 above guarantees that all thesefunctions are well defined and unique. Togetherwith standard profit-maximization conditionsthey also guarantee that the profit functionp(k,z; w) is (i) continuous, strictly increasing, andstrictly concave ink [ _; (ii) continuous andstrictly increasing inz [ Z; and (iii) continuousand strictly decreasing in the wage ratew . 0.

The cost of obtaining a stock of capitalk9 fornext period, given that the current stock isk,will be represented by the traditional investmentfunction i (k, k9): _ 3 _ 3 5:

(4) i ~k, k9! 5 k9 2 ~1 2 d!k, d [ @0, 1#.

The final aspect concerns the finance costs.This is a key assumption for our analysis. Ideallywe would prefer to model financial intermediationendogenously (as in Douglas W. Diamond, 1984,for example). This approach, however, would de-mand a far more complex model than the onenecessary to study the effect of intermediationcosts on investment behavior at the firm level.Therefore we choose to summarize this costlyactivity with a simple functional form capturingthe basic notion that external funds are costly.

Clearly a firm will only choose to use exter-nal sources as a last resource when currentinvestment opportunities justify the additionalcost. Alternatively, it is never optimal to issuenew securities while paying dividends. Thus thefinancing cost function has the form

(5) l 5 l~i ~k, k9! 2 p~k, z; w!!

5 l~k, k9, z; w!.

We make only very general assumptionsabout the nature ofl. In particular we assumethat these costs are positive and increasing ifthe firm uses external funds. If no externalfinance is required, these costs are zero. This

assumption can accommodate several specifi-cations of the cost function, possibly moti-vated by alternative interpretations of thenature of the financial imperfection.

ASSUMPTION 3: The financing cost functionl: 5 3 51 satisfies:(i ) @a # 0, l(a) 5 0;(ii ) @a . 0, l(a) . 0, l9(a) . 0.

Figure 3 depicts alternative representations ofthis function consistent with Assumption 3.

The dynamic nature of each firm’s problemshould be clear from the interaction of theinvestment decision with the Markov struc-ture for the productivity shock. Given therecursive structure of this environment it issimpler to define each firm’s problem usingdynamic programming. Letp(k, z; w) denotethe market value of a firm that has a capitalstock ofk and a productivityz, while facing awage rate equal tow. The dynamic problemfacing each firm is

(6) p~k, z; w! 5 maxk9 $ 0

Hp~k, z; w!

2 i ~k, k9! 2 l~k, k9, z; w!

1 b maxS ~1 2 d!k9, E p~k9, z9; w!D3 Q~dz9uz!J .

The right-hand side of (6) specifies thedecisions faced by this firm. The first threeterms reflect the current dividends: profitsminus investment spending and financing

FIGURE 3. FINANCING COSTS


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

(7) E p~k9, z9; w!Q~dz9uz! , ~1 2 d!k9.

In what follows we will focus solely onstationary equilibria, where all prices andaggregate quantities as well as the distribu-tion of firms across states are constant. Belowwe show that such equilibrium indeed existsand is unique. Thus we will assume thatw 5 w9.

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).

PROPOSITION 1:There is a unique functionp(k, z; w) that satisfies(6).

PROOF:See Gomes (2000).

PROPOSITION 2:The value function p(k, z;w) is (i ) continuous and increasing in(k, z),and (ii ) continuous and strictly decreasingin w.


Proposition 1 guarantees the existenceof a value functionp(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,denotedk(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! 5 minHarg maxk9 $ 0

Hp~k, z; w!

2 i ~k, k9! 2 l~k, k9, z; w!

1 b maxS ~1 2 d!k9, E p~k9, z9; w!

3 Q (dz9, z)DJJ.

Given the structure of the problem, the max-imizer on the right-hand side of (6) need not beunique. Equation (8) states that a firm choosesthe value that does not require external finance.2

Intuitively, if borrowing does not (strictly) raisethe value of the firm it is not used.

Since exit takes placebefore the shock isobserved, firms know in advance whether theywill choose to exit or not in the next period. Exitis therefore completely determined by the cur-rent state and can be summarized by a thresholdvalue for the idiosyncratic productivity level.The exit decision can be described as follows

(9) x~k, z; w! 5 H1 z . z* ~stay!0 z # z* ~exit!

where

(10) z* ~k, z; w!

5 minH infHz: E p~k9, z9; w!

3 Q~dz9uz! $ ~1 2 d!k9J , z#J .

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 enough

2 Only two solutions can exist for each state, one withand one without external finance. Clearly if the value of thefirm is the same in both cases and the value function isincreasing in capital, then the optimal investment choicemust be higher with external finance. Technically, (8) pro-vides a measurable selection of the optimal policycorrespondence.


to 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*.

Propositions 1 and 2 characterize the solutionto the individual problem of each firm for agiven wage ratew. The equilibrium level ofwis uniquely determined by the free-entry condi-tion:

(11) E p~0, z; w!w~dz! # 0.

This condition must hold with equality if entryis positive. In this case Proposition 2 guaranteesthat there is a unique value ofw that solves (11).The exact level of entry, denoted byB, is thendetermined by the market-clearing conditionsbelow.

B. Aggregation

With the description of individual firmbehavior complete we can now characterizethe aggregate variables for this economy.Since each firm can bedescribed by its currentindividual state (k, z), we can summarize the ag-gregate distribution of firms with a measure de-fined over this state space.

Formally we define the measurem such that@(k, z) [ _ 3 Z, m(k, z) denotes the mass offirms in the state (k, z). For any setQ 5 (K,Z) [ Jk 3 Jz, the law of motion for thismeasurem is given by

(12) m9~Q!

5 5T~Q, ~k, z!!m~k, z!, if k . 0

T~Q, ~0, z!!m~0, z!

1 B EZ

EZ

x~K!v~dz!Q~dz9uz!, if k 5 0

with

(13) T~Q, ~k, z!!

5 EZ

x~K!x~k, z; w!Q~dz9uz!,

and

(14)

x~K! 5 H1 if k~k, z; w! [ K ,

0 if k~k, z; w! ¸ K.

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 survivingfirms by combining the optimal decision rulesconcerning capital accumulation and exit. Itcomputes all the conditional transition prob-abilities in the product space_ 3 Z, wherethe conditioning event is that the firm sur-vives until next period. Naturally in a station-ary equilibrium we expect thatm9 5 m 5 m*.The invariant distributionm* summarizesthen the distribution of firms in a stationaryindustry equilibrium.

With this definition at 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 aggregate labordemand, total profits, and the aggregate invest-ment, defined respectively as

(15) Y~m, B; w! 5 E ~y~k, z; w! 2 f !

3 x~k, z; w!m~dk, dz! 2 Bf,

(16) L~m, B; w!

5 E l ~k, z; w!x~k, z; w!m~dk, dz!

1 B E l ~0, z; w!w~dz!,


(17) P~m, B; w!

5 E p~k, z; w!x~k, z; w!m~dk, dz!

1 B E p~0, z; w!w~dz!,

(18) I ~m, B; w!

5 E i ~k~k, z; w!, k!x~k, z; w!m~dk, dz!

1 B E k~0, z; w!w~dz!.

Similarly, total intermediation costs for thiseconomy are given by the function

(19) L~m, B; w!

5 E l~k, k~k, z; w!, z; w!

3 x~k, z; w!m~dk, dz!

1 B E l~0, k~0, z; w!, z; w!w~dz!.

Proposition 3 establishes that aggregatequantities are jointly linear homogeneous inthe level of entryB and the measure of firmsm. This property will be useful later when wecompute the competitive equilibrium of themodel.

PROPOSITION 3:All aggregate quantitiesY(m, B; w), L(m, B; w), P(m, B; w), I (m,B; w), and L(m, B; w) defined aboveare jointly homogeneous of degree one in Band m.


C. Households

The 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) maxc,l ,st ~kt ,zt ! $ 0

E0F Ot 5 0

`

b̃tU~ct , 1 2 l t !Gs.t. ct 1 E ~p̃t ~k, z!

2 dt ~k, z!!st ~k, z!m~dk, dz!

5 E max$p̃t ~k, z!, fk%st 2 1~k, z!

3 m~dk, dz! 1 wt l t,

wherec is consumption, andp̃t(k, z), dt(k, z),andst(k, z) denote the price, dividends, and thefraction of shares owned by the household, re-spectively. For convenience we assume thatdividends are paid just after shares are bought.Note that, since we are restricting ourselves to astationary measure of firmsm, the assumptionof a stationary equilibrium is implicit in thisformulation of the household problem. We sum-marize our (standard) assumptions about pref-erences in Assumption 4.

ASSUMPTION 4: The preference relation sat-isfies (i ) 0 , b̃ , 1, and (ii ) U(c, 1 2 l ):51 3 + 3 5 is strictly increasing, strictlyconcave, and twice continuously differentiable.

Under these assumptions it is easy to estab-lish that in a stationary equilibrium the discountrates for consumers and firms are the same, andthe price of a share,p̃(k, z), equals the value ofthe firm, p(k, z).

PROPOSITION 4:In equilibrium p̃(k, z) 5p(k, z) and b̃ 5 b.



Since all aggregate quantities and prices areconstant, the consumer problem can then befurther simplified into a static problem of theform

(21) maxc,l $ 0

U~c, 1 2 l !

s.t. c 5 wl 1 P~m, B; w!,

which is a standard concave problem withinterior solutions given by two optimal deci-sion rules for consumption and labor supply,denoted respectively byC(w, P(m, B; w))and Ls(w, P(m, B; w)).

D. Stationary Competitive Equilibrium

With the model complete we are now readyto state the conditions required to characterizea stationary competitive equilibrium for thiseconomy.

Definition 1: A stationary competitive equi-librium is a set of (i) allocation rulesLs(w, P(m, B; w)) and C(w, P(m, B;w)) for the representative household andk(k, z; w), l (k, z; w) and x(k, z; w) as wellas a value functionp(k, z; w) for eachfirm; (ii) aggregate quantitiesY(m, B; w),L(m, B; w), P(m, B; w), I (m, B; w), andL(m, B; w); (iii) a wage ratew; and (iv) ameasurem of firms and a level of entryB,such that:

● the consumer decision rules solve (21);● the firm decision rules and value function

solve (6) for each firm;● the free-entry condition (11) is satisfied;● markets clear:

(22) Ls~w, P~m, B; w!! 5 L~m, B; w!;

(23) C~w, P~m, B; w!! 5 Y~m, B; w!

2 I ~m, B; w! 2 L~m, B; w!;

● consistency: conditions (15)–(19) are satis-fied and the distributionm obeys the law ofmotion (12), withm 5 m9.

PROPOSITION 5:A stationary competitiveequilibrium with positive entry exists.


III. Stationary Equilibrium

Computing 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 determined either bymatching properties of the model to U.S. data orby using prior empirical evidence. Second, be-cause exact analytical solutions are impossibleto obtain in this environment, we need to de-velop a numerical algorithm capable of approx-imating the competitive equilibrium up to anarbitrarily small error. Gomes (2000) providesthe details on this procedure. The final step is toimplement 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 preferences are not cru-cial to our analysis we will take a minimalistapproach and summarize household behaviorwith a momentary utility function similar to thatin Gary D. Hansen (1985):

(24) U~c, l ! 5 log c 1 H~1 2 l !.

This function has the convenient property thatlabor-supply decisions are independent from thelevel of wealth and from the real interest rate.Given this specification we only need to assign


parameter values tob, the intertemporal dis-count factor, andH, which is determined by thefraction of workers in the population. In thesteady state the real interest rate equalsr 51/b 2 1. Over the last century this value hasaveraged about 6.5 percent per year, thus we setb 5 1/1.065. Since the share of employed work-ers in the labor force equals about 60 percent,we choose this value for the parameterH.

Technology.—To completely specify the pro-duction technology of this economy we need tochoose a functional form for the productionfunction and the stochastic process for the pro-ductivity shocks. We also need to assign param-eter values for the investment function, the sunkcost of entrants and the fixed cost of production.

We start by assuming that production takesplace in each firm according to a decreasingreturns Cobb-Douglas production function

(25) y 5 A«zkakl a l 0 , a l 1 ak , 1.

With this specification we need only to assignvalues forak and a l, the two output elastici-ties.3 To do this we need first to determinate thedegree of decreasing returns in the economy andthen one of the two elasticities. Using disaggre-gated data for manufacturing industries, CraigBurnside (1996) estimates returns to scale to bejust under 1. Therefore we seta l 1 ak 5 0.95,a value that does not depart substantially fromthe standard CRS assumption. Since the laborshare of income has averaged about 0.65 overthe postwar period, we seta l 5 0.65,implyinga value ofak 5 0.3.

The stochastic process for the level of tech-nology for incumbents is assumed to be de-scribed by the relation

(26) z9 5 rz 1 «9,

where « is assumed to follow a (truncated)normal distribution with 0 mean, standard devi-ation of s and finite support [24s, 4s]. Theinitial level of technology for entrants is as-

sumed to follow a uniform distribution overZ 5 [24s/=1 2 r2, 4s/=1 2 r2].4

The parametersr ands have implications forthe degree of persistence and dispersion in thesize distribution of firms. We thus restrict theirvalues 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).5

In our benchmark model this implies choosingvalues ofr 5 0.62 ands 5 0.15.

Similarly, the rate of depreciation in the cap-ital stock is set to equal 0.12 so that the modelmatches the average investment to capital ratiofound in the data.

Finally, we are left with the fixed cost ofproduction f. Given the degree of returns toscale, the nature of the financing costs and thestructure for 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 anunbalanced panel with significant firm turnover.We will quantify f to match this fact closely ineach simulation.

Financing Costs.—Modeling the costs of ex-ternal finance is a somewhat more complicatedissue and requires some caution. Financial mod-els usually focus on two types of costs associ-ated with this activity: informational costs andtransaction costs. Informational costs are relatedto the extra premium that is associated with thebad signal that a firm may transmit to the marketwhen trying to raise funds as well as the dete-rioration in balance sheet. These costs are veryhard to quantify and the number of empiricalstudies that address the issue is very limited.Transaction costs are generally associated withthe compensation to intermediaries plus all thelegal, accounting, and other bureaucratic costs.Constructing quantified measures of these costshave been the subject of much research. Giventhe availability of data we will focus solely ontransaction costs as a source of imperfection infinancial markets.

Clifford W. Smith, Jr. (1977) provides de-3 The parameterA is introduced only to scale the capital

stock. In each simulation we 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 description of the data see the Appendix.


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 quantitative measure of thesecosts we fit a linear cost function of the type

(27) l 5 l0 1 l1 3 NewIssues

to this data and obtain the following results forthe total costs of raising new equity (units inmillions of U.S. dollars):

(28) l 5 0.481 0.0283 NewIssues.

Since this regression fits the data quite well(this should be expected given the pattern ofaverage costs depicted on Figure 4) we chooseto specify this functional form for the unit costfunction and use our regression results to setl1 5 0.028. Since the intercept term is sensitiveto the unit of measurement, a better measure forl0 can be obtained by looking at the averagecost for very small issues. These average about0.108, implying an intercept term ofl0 5 0.08,a value that we adopt. We will examine the

consequences of adopting alternative assump-tions on the nature and the magnitude of thesecosts later.

Table 1 summarizes our benchmark calibra-tion procedure.

B. Results

Optimal Firm Decisions.—Before character-izing the equilibrium and the full cross-sec-tional distribution of firms in this economy, it ishelpful to develop some intuition about optimalfirm behavior. Figure 5 provides a very simplequalitative illustration of the combined finance-investment decisions. This representation high-lights a few of the interesting features of thiseconomy. First, only firms with relatively lowlevels of productivity leave the market in anygiven period. Second, external financing is usedonly by those firms who are either very small or

FIGURE 4. COSTS OFISSUING SECURITIES

Note: The top line signifies underwriting; the middle linesignifies rights with standby; the bottom line signifies rights.

TABLE 1—CALIBRATION

ParameterBenchmark

value Empirical restriction

Technologyak 0.3 Degree of returns to scalea l 0.65 Labor shared 0.145 Investment to capital ratio

Technology Shockr 0.762 Persistence in investments 0.0352 Cross-section variance of

investmentFinancing Costs

l0 0.08 Fixed flotation costsl1 0.028 Unit flotation costs

Preferencesb 1/1.065 Interest rateH 0.6 Employment share

FIGURE 5. FIRM BEHAVIOR


very productive (the “borrowing” firms). Theexplanation is simple: in the absence of fric-tions, productive firms would 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 profitable toaccept 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; firms use external financeinfrequently (about once in every sevenyears); and (ii) an indirect “size” effect; ifexternal funds are required, they are raised invery large quantities.

Firm Behavior.—Table 3 focuses on the mi-croeconomic implications of the model by ex-amining some summary statistics from thecross-sectional distribution of firms. The firstpart of the table contains those variables that themodel was calibrated to approximately match inthe numerical exercise. Unfortunately, the highdegree of nonlinearities in the solution makes itnearly impossible to match these moments ex-actly. Nevertheless we see that our approxima-tion appears quite reasonable along thosedimensions.

The second half of the table concerns themodel’s ability to replicate other interesting fea-tures of the data and thus provides a moreinteresting measure of the empirical success ofthe model. Consistent with the early findings ofEric B. Lindenberg and Ross (1981), as well asseveral other more recent studies, we find thatthe model implies average values ofq consis-tently above 1 on average. Here this is a con-sequence of industry selection: the survivingfirms in the sample are the most profitable ones.In addition, the model does a reasonably goodjob of replicating some features regarding thebehavior of cash flow. Given the role thatq andcash flow play in the investment regressionsbelow, this is an important finding.

The Role of Financing Constraints.—Table 4examines the role of financial constraints. It iseasy to see that they are clearly nontrivial in thebenchmark economy: over half of all the firmsare constrained according to our definitionabove. Although these firms are somewhatsmaller than the average unconstrained firm, itappears that the significance of financing con-

TABLE 2—AGGREGATE RESULTS

Variable Model

Investment share (I /Y) 0.21Share of financing costs (L/Y) 0.0062External finance/total costs 0.17Flotation costs/external finance 0.39

TABLE 3—CROSS-SECTIONAL RESULTS

Variable Data Model

Matched quantitiesAverage size (capital) 80.89 80.89Investment rateI /K 0.145 0.145Standard deviationI /K 0.139 0.160AutocorrelationI /K 0.239 0.191

Other quantitiesMeanq 1.56 1.12Growth rate (sales) 0.036 0.031AverageCF/K 0.292 0.221Standard deviationCF/K 0.214 0.091Negative investment (fraction) 0.08 0.13

Note: CF denotes cash flow


straints is essentially determined by the individ-ual productivity (z) and not the size of the firm(k). This becomes clear from examining thenext rows: constrained firms have a higher mar-ginal productivity of capital and invest morethan those unconstrained. They also have ahigher value of Tobin’sq on average.

Marginal productivities provide an addi-tional insight into the model. The marginalproductivity of capital for constrained firms isactually higher than the rental price of capital(r 1 d 5 0.21), thus they do not satisfy astandard Euler equation. Unconstrained firmson the other hand are relatively unproductive.On average, however, they do not satisfy theEuler equation either: they overaccumulatecapital, as evidenced by the low marginalproduct.6,7 A 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 problem with the analysis aboveis that, in practice, we can not determine exactlywhich firms are financially constrained. A com-mon empirical proxy for this is firm size. Weexamine the results of applying this procedureto our model in Table 5. We separate firms intwo categories: “small” firms, with a capitalstock below the sample average, and “large”firms, those whose size is above the marketaverage.

An interesting feature of this model is itsability to replicate the negative correlation be-tween firm size and firm growth, extensivelydocumented by many authors (for example,David S. Evans, 1987; Bronwyn H. Hall, 1987).Small firms are growing faster as evidenced bythe larger investment to capital ratio. Rememberthat in our model, size depends on profitability:firms become large only because they had avery good history of technology shocks. Be-cause technology levels are mean reverting theymust, at least on average, grow at a slower ratethan small firms. Small firms on the other handappear more risky with very large annual exitrates. Despite the fact that more small firms facefinancing constraints, the size of the firm ap-pears as a very imperfect proxy for the existenceof financing constraints. There are two reasonsfor this: (i) the persistence in 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 financially constrained.8

6 This subgroup includes a large fraction of the exitingfirms which explains the large average drop in investment inthis sample.

7 This 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 resultsabout the absence of cash-flow effects. Results for aversion of the model with cash holdings are available uponrequest.

8 This fact is also documented by some Euler-equation-based tests of financing constraints (see Whited, 1992, forexample).

TABLE 4—FINANCE

Variable External finance Constrained Unconstrained

Firms 0.07 0.63 0.30Share of investment 0.79 0.74 20.53Size (capital) 55.96 171.93 298.57Mean I /K 1.20 0.188 20.086Tobin’s q 1.34 1.14 1.08Marginal product of capital 0.24 0.22 0.19

TABLE 5—FINANCE AND SIZE

Variable Small firms Large firms

Fraction of firms 0.72 0.28Share of investment 0.85 0.15Size (capital) 139.80 359.79Mean I /K 0.185 0.035Fraction constrained 0.61 0.39Exit rate 0.12 0.01Tobin’s q 1.12 1.15Marginal product of capital 0.21 0.22


IV. Empirical Implications

A. Investment Equations

The equilibrium distribution generated by 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 the relevance of finance con-straints. The empirical methodology is tospecify a functional form for investment of thetype

(29)i i ,t

ki ,t 2 15 b0 1 b1qi ,t 2 1

1 b2

p i ,t 2 1

ki ,t 2 11 ft 1 di 1 « i ,t

where

(30) qi ,t 5pi ,t

ki ,t

andp is the market value of the firm defined in(6). Hence we are using beginning of periodaverageq and beginning of period cash flow inthese regressions;ft is a year effect anddidenotes a firm-specific fixed effect. The yeareffects are introduced to eliminate the effects ofbusiness cycles in the regression.

Empirical Results.—The basic source for ourempirical analysis is the Compustat data set. Weuse the combined annual, full coverage, andresearch 1998 files. We start our sample in 1979since the coverage of over-the-counter firmsincreased substantially after this year, giving usa much larger cross section of firms.

Substantial changes in reporting and account-ing methods lead us to stop the sample in 1988(for details, see Ben S. Bernanke et al., 1990).The total number of firms in this sample forthese years is 9,761. This number is 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 unbalanced panel of 12,321 firm-yearobservations.

The second column of Tables 6 and 7 docu-

ments the results of estimating equation (29) infirst differences with and without imposingb2 5 0.9

As others before us we also find a “cash-floweffect”: the cash-flow regressor appears to sub-stantially improve the predictive power of theregression as the adjustedR2 also improvessubstantially when 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 number offirms 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.10 Finally we repeatthis procedure 1,000 times and report thesample means for both coefficients, the stan-dard errors, and the adjustedR2.

9 This procedure is commonly employed as possiblecorrection of measurement error in several studies.

10 Year effects are not necessary since we are only look-ing at a nonfluctuating economy. Nevertheless this is veri-fied for the artificial data.

TABLE 6—STANDARD INVESTMENT EQUATIONS

Coefficient DataBenchmark

modelNo financingconstraints

b1 0.06 2.82 8.07(0.01) (0.08) (0.10)

R# 2 0.12 0.53 0.84

Note: Standard errors are in parentheses.

TABLE 7—CASH-FLOW-AUGMENTED EQUATIONS

Coefficient DataBenchmark

modelNo financingconstraints

b1 0.06 4.13 11.52(0.01) (0.39) (0.05)

b2 0.14 22.67 210.19(0.04) (0.77) (0.10)

R# 2 0.25 0.53 0.98



The results for our benchmark model areshown in the third column of Tables 6 and 7.We obtain three conclusions from this exercise.First, relative to the standard neoclassical modelwe find that our benchmark calibration deliversa much lower correlation betweenq and invest-ment. This is not very surprising given that wehave departed substantially from the strong ho-mogeneity assumptions often imposed in theliterature. As a result, the proper characteriza-tion of the investment decision of each firm willnot, in general, resemble a simple linear func-tion of averageq. Given the empirical failure ofsimpleq models, this is probably a good result.Second, the coefficient onq is much higher thanin the data. This result was also documented bySargent’s (1980) early study and should not bevery surprising as the optimal investment deci-sions in this model follow some type of (s, S)behavior and involve some dramatic, althoughinfrequent, changes in investment rates at sometrigger points. It is well known that one caneasily eliminate this problem by introducingsome additional convex adjustment costs oninvestment. Since our goal is to understand the“cash-flow effect” and not to replicate individ-ual coefficients we abstract from these for sim-plicity. Third, and more importantly, we do notfind evidence of a cash-flow effect. Unlike ourempirical results, the cash-flow-augmented re-gressions add no significant explanatory powerto the investment equation. Although financialconstraints are very important for many firms,as we have seen in Table 4, the independentinformational content of cash flow appears quitesmall.11

The last column is the most convincing: itshows the results of estimating (29) for a modelwith no financing constraints at all.That is, forthis model we have set the functionl[ equal to

zero everywhere. Here however we do find acash-flow effect. The implication of these re-sults is quite apparent: not only is the existenceof financial constraints not sufficient to estab-lish cash flow as a significant regressor beyondaverageq, but it also appears not to be neces-sary. This is an important result. It is natural thatwe may ask whether it survives alterations inour benchmark model.

Alternative Samples.—To better understandour results it is instructive, however, to firstreplicate regression (29) for alternative sub-samples of firms. In particular we considersix common types of subsamples: “balancedpanel” 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” firms is only possible in themodel.

Tables 8 and 9 illustrate two main results.12

First, we find no evidence of strong cash-floweffects, with the possible exception of the “un-constrained” and “small” samples. The resultfor unconstrained firms 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 subsample of “constrained” firms. Againthis is a very strong result. Taken together thesetwo results are again very suggestive of the(lack of) statistical power of these regressions asa useful means of identifying financially con-strained firms.

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 ofqdoes 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.

11 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 from convex adjustment costs in this model,the regression coefficients will be generally quite large.Second, as we will see below, with technology shocks cashflow becomes highly correlated withq. Third, the equationis badly misspecified due to the (generally) highly nonlinearnature of investment decisions. All these render the esti-mated coefficients on these linear equations rather uninfor-mative. Instead we choose to focus on the adjustedR2 as abetter indicator of additional informative content of thecash-flow regressor.

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


B. Alternative Specifications

We now examine the robustness of our find-ings by extending the benchmark model alongseveral dimensions. Although the quantitativedetails change across different specifications,the strong qualitative message remains: infor-mation about financing constraints should becaptured by the (appropriately measured)q re-gressor and cash flow is essentially redundantand uninformative.

Alternative Financing Constraints.—Thecalibration of the functionl[ that describesthe costs of raising external finance 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 ofl[.

In this section we consider two alternativespecifications of the financing costs functionl[. While these are not exhaustive theycover 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 interpretl[ as the differencebetween a “borrowing” rate (r 1 l), at whichexternal funds can be obtained from banks,and a “lending” rate (r ), implicit in the op-portunity cost of internal funds to firms. For-mally we impose

(31) l 5 0.023 Borrowing.

The interest rate spread is then set at 2 per-cent, the average spread between six-monthCDs (lending rate) and the prime rate (borrow-ing rate) for the period 1968–1997.13

An alternative experience is to focus on therole of the fixed costs in the functionl[. To doso let

(32) l 5 0.15.

13 An alternative would be to use the rate of commercialpaper instead of the prime rate. This would imply an interestrate spread of around 0.5 percent. However, many firms donot have access to commercial paper. In addition, a modelwith such a small interest rate spread is very similar to themodel without financing constraints discussed above.

TABLE 8—STANDARD INVESTMENT EQUATIONS: SUBSAMPLES

Coefficient Data Balanced panel Constrained Unconstrained External finance Large Small

b1 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)

R# 2 0.12 0.58 0.99 0.34 0.98 0.74 0.71


TABLE 9—CASH-FLOW-AUGMENTED EQUATIONS: SUBSAMPLES

Coefficient Data Balanced panel Constrained Unconstrained External finance Large Small

b1 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 0.14 212.57 1.13 222.48 217.13 25.82 237.60(0.04) (0.70) (0.24) (1.54) (1.00) (0.66) (4.98)

R# 2 0.25 0.61 0.99 0.52 0.99 0.77 0.83



This specification is somewhat similar to thoseused in the investment with fixed cost literature.Note that the fixed cost is about 50 percenthigher than in the initial calibration.

The results of estimating equation (29) for thesealternative models are displayed in columns 3 and4 of Tables 10 and 11. We find that the linearequation is a poorer fit when fixed costs are veryhigh. Again this is because high fixed costs giverise to very discontinuous investment decisions.Eliminating the fixed costs, on the other hand,improves the overall quality of the fit. Regardless,the adjustedR2 still changes very little with theinclusion of cash flow in the regressions. Againwe see no evidence of a strong cash-flow effect inthe artificial data.

Marginal q.—The final column of Tables 10and 11 looks at the performance of an alterna-tive specification of equation (29) that uses mar-ginal, instead of average,q as a measure offundamentals for the benchmark model. We de-fine marginalq as the right-hand derivative ofthe value functionp(k, z).

(33) Limh3 01

p~k 1 h, z! 2 p~k, z!

h.

We find that, as first documented by Cabal-lero and John V. Leahy (1996), averageq canactually perform much better than marginalq inthese reduced-form equations. This is a conse-quence of the discontinuity in the investmentdecision of the firm in the presence of fixedcosts. Caballero and Leahy (1996) show that inthis case, investment is not even a monotonicfunction of marginalq. In the context of ourbenchmark calibration we find that it is actuallypossible to obtain an overall negative correla-tion between the two variables.

The weak performance of marginalq ex-

plains the success of cash flow in this regres-sion. Again, however, we argue that this is soonly because we have a very poor measure offundamentals.

C. Productivity Shocks, Cash Flow,and Investment

The robustness of the previous results isstriking. Despite the important role 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 provide us with some of theintuition behind these results. They depict thecross correlations between 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 collinearitybetweenq, cash flow, and also sales, here justequal to output. Moreover all of these vari-ables are also strongly correlated with thetechnology shock as well. As Sargent (1980)pointed out, this is important because in thecontext of a fully specified general-equilib-rium model with productivity shocks the stan-dard investment regressions are generally notjustified on theoretical grounds as both the

TABLE 10—STANDARD INVESTMENT EQUATIONS:ALTERNATIVE SPECIFICATIONS

Coefficient Data

Financing costsMarginal

qVariable only Fixed only

b1 0.06 2.92 2.82 20.86(0.01) (0.07) (0.11) (1.03)

R# 2 0.12 0.61 0.32 0.06


TABLE 11—CASH-FLOW-AUGMENTED EQUATIONS:ALTERNATIVE SPECIFICATIONS

Coefficient Data

Financing costsMarginal

qVariable only Fixed only

b1 0.06 4.88 6.25 20.22(0.01) (0.29) (0.50) (0.45)

b2 0.14 24.11 27.00 5.41(0.04) (0.59) (1.00) (0.16)

R# 2 0.25 0.63 0.35 0.50


14 With the exception of cross correlations with invest-ment, which are usually a little higher, the results arequantitatively very similar for the other subsamples that wehave studied.


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 stronglycorrelated amongst themselves, one can expectthat measurement error in one of them (q, forexample) may lead an econometrician to assigna larger role for the others (cash flow and salesusually) in the regression. As our exercisesdemonstrate however, this is, essentially, with-out economic significance.

D. Measurement Error

The results above are important in two ways.First, they make it clear that the existence offinancial constraints is not sufficient to establishcash flow as a significant regressor, beyondq.In the context of a fully specified model, theeffect of financial constraints must bealreadyincluded in the market value of the firm andshould also be captured byq. Second, the col-linearity between cash flow andq suggests thatany sizable measurement error in the construc-tion of q can reduce the overall correlationbetweenq and investment and perhaps generatea cash-flow effect.

In this section we explore these ideas byanalyzing the effects of measurement error onour 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 severalidentifiedby researchers in empirical studies.

To consider this we provide yet another ex-tension of the benchmark model with stochasticprices for investment goods. Specifically weassume that investment goods can be trans-formed into consumption goods at the relativepricef. This rate of transformation is stochasticand firm specific, reflecting idiosyncratic shocksto the value of the firm’s capital stock. Theshock to the value of investment goods wascalibrated using data from Jeremy Greenwoodet al. (1997) on the behavior of the relative priceof investment goods. They estimate that the(detrended) price of investment goods followsthe process

(34) f9 5 f# ~1 2 0.64!

1 0.64f 1 «, s« 5 0.035,

wheref# , the average value of capital goods inunits of consumption goods, is normalized to 1.We assume that these values hold for our modelas well and restrict the distribution of the inno-vations to be normal for incumbents and uni-form for new entrants. While this calibrationprocedure is not theoretically correct it is nev-ertheless used to provide a simple illustration ofthe effects of measurement error in cross-sectional investment regressions.

TABLE 12—CROSSCORRELATIONS:BENCHMARK MODEL

Variable InvestmentTobin’s

qCashflow Sales exp(z)

Investment 1.00 0.53 0.57 0.56 0.53Tobin’s q 1.00 0.92 0.93 0.92Cash flow 1.00 0.99 0.96Sales 1.00 0.95exp(z) 1.00

TABLE 13—CROSSCORRELATIONS:NO FINANCING CONSTRAINTS

Variable InvestmentTobin’s

qCashflow Sales exp(z)

Investment 1.00 0.45 0.45 0.48 0.42Tobin’s q 1.00 0.95 0.97 0.95Cash flow 1.00 0.99 0.98Sales 1.00 0.97exp(z) 1.00


To introduce measurement error in the capitalstock we assume that the econometrician cannot observe the actual price of the investmentgoods,f, and simply estimates this to be con-stant across firms and equal to its average valueof 1.

The results of this procedure are documentedin the third column of Tables 14 and 15. Whileall correlations are now lower, we observe thatcash flow does increase the overall explanatorypower of the regression. While the improve-ment is not dramatic here it illustrates the po-tential of the measurement-error argument. Inthis case the success of the cash-flow regressoris clearly identified from our theoretical con-struction. It is only due to the problems associ-ated with the construction of theq variable thatwe obtain significant cash-flow effects.

A more direct alternative is perhaps to exam-ine the effects of introducing classical measure-ment error in averageq. As a simple illustrationsuppose that there is some normally distributednoise that prevents the econometrician fromhaving an exact measure of averageq. Specif-ically, suppose that the econometrician observesonly

(35) q̃ 5 q 1 j, j , N~0, sj2!.

We then setsj2 equal to1⁄10 of the variance of

q, 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 measurement error: lowercoefficients onq and lowerR# 2 as well. Inter-estingly the cash-flow effect also seems strongerin this case.

Finally we also show the results of introduc-ing classic measurement error for the modelwithout financing constraints. Again these con-firm that financing constraints are not necessaryto observe cash-flow effects, in the sense thatthe adjustedR2 increases significantly.

The conclusion from these experiencesseems, by now, quite clear: regardless of themodel the existence of financial constraints isneither sufficient nor necessary to establish cashflow as a significant regressor, beyondq. Thecash-flow effects are either a combination of theartificial correlation induced by the technologyshocks and the measurement error inq or aconsequence of the nonlinearities in investmentand the poor fit of (29).

V. Conclusions

Macroeconomists often emphasize the roleof financial constraints as an important sourceof propagation of shocks across time andfirms. Moreover, recent work by Bernankeand Alan S. Blinder (1988), Anil K Kashyap

TABLE 14—STANDARD INVESTMENT EQUATIONS: MEASUREMENT ERROR

Coefficient DataMeasurement error

Capital stockMeasurement error

ClassicalMeasurement error

No constraints

b1 0.06 2.08 1.59 6.71(0.01) (0.24) (0.08) (0.12)

R# 2 0.12 0.29 0.18 0.73


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

Coefficient DataMeasurement error

Capital stockMeasurement error

ClassicalMeasurement error

No constraints

b1 0.06 0.65 0.45 8.19(0.01) (0.61) (0.09) (0.14)

b2 0.14 1.25 4.72 25.35(0.04) (0.40) (0.22) (0.32)

R# 2 0.25 0.39 0.46 0.81



et al. (1993), Bernanke et al. (1997), andThomas F. Cooley andVicenzo Quadrini (1998)suggests that in the presence of these constraints,monetary policy can have powerful effects onindividual firm decisions and aggregate condi-tions. Much of the evidence on the role of financ-ing constraints at the firm level relies on the resultsof estimating cash-flow-augmented investmentequations like (29).

This work questions the conclusion that one cansafely attribute the empirical success of cash flowto the importance of financing constraints in in-vestment decisions by firms. We do so by address-ing this issue from a different, more structural,perspective. We begin by fully specifying a modelof investment under financial constraints consis-tent with several empirical regularities about firmbehavior observed in the data.

We obtain three main findings from this ar-tificial panel of firms. First, despite the presenceof liquidity constraints, it is hard to find evi-dence that cash flow adds significant explana-tory power to the investment regressions. Thusthe existence of financial frictions is not suffi-cient to obtain significant cash-flow effects. Weargue that, in the context of a fully specifiedmodel, the effect of financial constraints shouldbe included in the market value of the firm andthus captured by a good measure ofq. Second,financing constraints are also not necessary toobtain these cash-flow effects in the model. It ispossible to construct simple examples wherecash flow adds some predictive power to invest-ment equations, even in the absence of financialfrictions. Third, as Sargent (1980) and Shapiro(1986) documented, we find that, in the contextof these general-equilibrium models, the corre-lation between investment, cash flow, and salesis quite artificial and a reflection of the under-lying technology shocks. Clearly this impliesthat the focus on reduced-form investmentequations can be quite problematic. In a relatedpoint, we also find that it is also possible toobserve cash-flow effects solely due to the mis-specification induced by fitting a linear equationto a nonlinear decision rule.

These results suggest that the presence ofmeasurement error in one of these variablesmay lead an econometrician to assign a largerrole to others. We formally confirm this conjec-ture by explicitly examining the effects of mea-surement error in investment regressions.

These findings, however, do not question the

existence or the importance of these constraintsfor investment decisions and/or the propagationof monetary policy shocks. It may well be thatthese constraints are relevant in practice. In fact,this approach to modeling equilibrium invest-ment and financing behavior, can be extended toaccount for aggregate business cycles and mon-etary policy shocks thus providing an ideal lab-oratory to study the importance of these effects.

Nevertheless our results highlight the enor-mous difficulties in using standard investment re-gressions in practice, and cast serious doubt on thecommon interpretation of cash-flow effects as ev-idence in favor of financing constraints.

APPENDIX

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

A. Variables

Investment.—Investment expenditures,I i ,t, isspending on plant, property, and equipment mi-nus capital retirements.

Capital Stock.—We use the perpetual inven-tory method described in Michael A. Salingerand Summers (1983) to convert the book valueof the gross capital stock into its replacementvalue:

(A1) Ki ,t 5 FKi ,t 2 1S Ptk

Pt 2 1k D 1 I i ,tG ~1 2 2/Lt !,

where the recursion is started with the reportedvalue of the capital stock in the first year thefirm is in the Compustat files,Pt

k denotes theprice of capital goods, taken to be the deflatorfor nonresidential fixed investment from DRI(Standard & Poor’s, 1999b), andLt is the aver-age life of capital goods computed using thedouble declining balance method as

(A2) Li ,t 5Ki ,t 2 1

r 1 I i ,t

DEPi ,t,

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


with Ktr denoting the reported value of the cap-

ital stock at periodt.

Market Value.—Market value of a firm,Vi ,t,is constructed as

(A3) Vi ,t 5 Di ,t 1 Ei ,t 2 INVi ,t,

whereEi ,t is the market value of equity,Dt isthe value of short- plus long-term debt, andINVt is the end-of-period value of inventories.The market value of equity is the sum of com-mon equity (number of shares outstanding timesthe end-of-period market price) plus preferredequity (firm preferred pay-out divided by S&P’spreferred dividend yield, from the DRI data set).

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

(A4) Qi ,t 5Vi ,t 2 1

Ki ,t 2 1.

Cash Flow.—Cash flow is defined as the sumof operating income and depreciation for theperiod.

B. Sample Selection

Most previous studies document a number ofirregularities in the sample period described,such as mergers, reporting, and/or coding errorsetc.16 To maintain comparability with the exist-ing literature we use the following procedure toeliminate extreme observations:

● The capital stock must be positive in allperiods;

● Investment can not exceed beginning of pe-riod capital stock;

● Tobin’s q must be positive and can not ex-ceed ten;

● Cash flow (in absolute value) can not exceedfive times the capital stock;

● The capital accumulation equation must besatisfied.

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