On the determinants of firm leverage: evidence from a structural estimation

19 Pages·2015·0.31 MB·English

by  Amilcar Menichini

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On the determinants of firm On the
determinants
leverage: evidence from a
of firm
leverage
structural estimation
179
Amilcar Menichini
Graduate School of Business and Public Policy, Naval Postgraduate School,
Received19April2014
Monterey, California, USA
Revised5September2014
Accepted18September2014
Abstract
Purpose–Thepurposeofthispaperistoinvestigatethephenomenaofconvergenceandstabilityof
leveragereportedbyLemmonetal.(2008).
PT) Design/methodology/approach – A dynamic trade-off model of the firm was used to simulate
5 ( investment, leverage, and payout decisions for different types of firms. From an econometric
1
0 standpoint,theEfficientMethodofMomentswasusedtorecoverthestructuralparameters.
2
y Findings – The structural model generates a leverage ratio that oscillates around a long-run,
a
M time-invariant level and consistently reproduces the convergence and stability of leverage reported
25 byLemmonetal.(2008).Themodelalsosuggeststhecausesofthoseobservedpropertiesofthedata.
54 That is, convergence is due to the mean-reversion of profits while stability is due to the different
8: fundamentalcharacteristics(e.g.capitalelasticity,volatilityofprofits,etc.)ofthefirm.
0
At Practicalimplications–Determiningtheoptimalcapitalstructureofafirmisacomplexproblem
n thathaschallengedacademicsandpractitionersforalongtime.Understandingleveragedecisionsisof
a
hig greatimportancenotonlyforfinancialmanagers,butalsoforinvestors,suchasbanks,debt-holders,
Mic equity-holders,andothercapitalproviders,whoneedtounderstandhowfirmsmakecapitalstructure
y of dOerciigsiionnasliitny/ovradleureto–aTchhieevauetahnoresffhicoiwensttahlalotctahteiofnirmof-sfpuencdifsi.cfixedeffectsinleverageregressionsare
sit not related to the usual determinants (e.g. profitability, market-to-book ratio), but to the primitive
ver characteristicsofthefirm(e.g.elasticityofcapitalintheproductionfunction,thevolatilityofprofits,
ni thecapitaldepreciationrate,theincometaxrate,etc.)
U
y KeywordsTrade-offtheory,Dynamicstructuralmodel,Efficientmethodofmoments,
b
d Firmleveragedeterminants,Speedofmean-reversion,Structuralestimation
e
ad PapertypeResearchpaper
o
nl
w
Do I provide further evidence on the determinants of corporate capital structure by
estimating a dynamic trade-off model of the firm that includes investment, leverage,
and payout decisions. The structural model generates a leverage ratio that oscillates
around a long-run, time-invariant level and consistently reproduces the convergence
andstabilityofleveragereportedbyLemmonetal.(2008).Thedynamicmodelsheds
light on the role played by the primitive characteristics of the firm (e.g. production
technology)toexplainthecross-sectionalvariationincapitalstructure.IuseEfficient
Method of Moments (EMM) to recover the structural parameters.
Thequestionaboutthedeterminantsofleverageiscentralincorporatefinance,but
researchershavenotyetreachedaconsensusaboutit.Severalstudies(e.g.Titmanand
Wessels, 1988; Rajan and Zingales, 1995; Frank and Goyal, 2009, and many others)
reportdifferenttime-dependentfirmcharacteristicsthatpartiallyexplainthevariation
in firm leverage. Lemmon et al. (2008) show that, even after introducing all InternationalJournalofManagerial
Finance
those determinants, most of the heterogeneity in capital structure is explained by Vol.11No.2,2015
pp.179-197
©EmeraldGroupPublishingLimited
JELClassification—G32,G35 DOI10.1108/IJMF-04-21071443--09015342
IJMF firm-specificfixedeffects.Thatis,theyfindthatwhereastraditionaldeterminantshelp
11,2 to understand the evolution of leverage over time, most of the variation in capital
structure across firms is captured by firm-specific fixed effects. I derive a dynamic
model of the firm to study leverage decisions and show that it produces results
consistent with those of the latter. My structural model allows me to explain the
primitive firm characteristics underlying the aforementioned fixed effects.
180 The dynamic model in the present paper is based on the trade-off theory of capital
structure and, therefore, explicitly captures the effect of leverage on firm value
introducingthebenefits(i.e.interesttaxshields)andcosts(i.e.costsoffinancialdistress)
of debt. The model produces leverage ratios that fluctuate around a long-run, time-
invariant level as the firm receives different profit shocks over time, as reported by
FlanneryandRangan(2006).Thismean-reversionofleverageisduetoboththeactive
managementofthedebt-equityratiobythefirmandthemean-reversionofprofitshocks.
Iusethemodeltoconstructapanelofdifferenttypesoffirmsandshowitgenerates
T) the leverage patterns found by Lemmon et al. (2008). Being structural, my approach
P
5 ( allowsmetoshedlightoncertaindeterminantsoffirmleveragethatarenotcaptured
1
20 by the latter. First, I reproduce their leverage regressions and find that the dynamic
ay model consistently replicates their results. The power of traditional determinants of
M
5 capital structure, mainly profitability and market-to-book ratio, to explain leverage
2
4 decisions turns out to be fairly small, while most of the variation in leverage across
5
8: firmsisexplainedbythefixedeffectsaroundwhichleverageoscillatesforeachtypeof
0
At firm in the panel. The structural approach I follow allows me to explain the key
n determinantsofthosefixedeffects.Viaasensitivityanalysis,Ishowthat,inmymodel,
a
g
hi these values are determined by the primitive characteristics of the firm, such as
c
Mi the volatility of profits, the elasticity of capital, the rate of depreciation of capital,
of and the income tax rate.
sity Second,Iinvestigatethepatternsofconvergenceandstabilityofleveragereported
er by Lemmon et al. (2008). I show that these observed properties of the data appear in
v
ni thecontextofmydynamicmodelandprovideasimpleexplanationforthem.Byusing
U
y the simulated panel, I construct both the actual and “unexpected” leverage portfolios
b
d andfindthatthedynamicmodelreplicatestheirresultsveryclosely.Inthecontextof
e
d
a thedynamicmodel,convergenceofleverageisgeneratedbythefactthatfirmleverage
o
wnl decisionsaremean-reverting.Thus,whenaveragedintothefourportfolios,firmswith
Do relatively high (low) leverage tend to return to more moderate levels of leverage
over time. Leverage stability refers to the observation that firms with relatively high
(low) leverage tend to keep relatively high (low) leverage for long periods of time.
This feature of the data appears in the context of the dynamic model because the
leverageratioofeachfirmtypeinthepanelmean-revertstoadifferentconstantvalue.
Consequently,thelong-runvaluestowhichthefourportfoliosconvergearetheaverage
of the unconditional means of leverage decisions of all firms included in the
corresponding portfolio. As before, these results suggest that the firm-specific fixed
effects explain most of the cross-sectional variation in leverage, and the power of the
usualtime-varyingdeterminantstoexplainsuchvariationisfairlylimited.Inthecontext
ofmymodel,thosefixedeffectsaredeterminedbythefundamentalcharacteristicsofthe
firmIdescribedinthepreviousparagraph.
Finally,Iusethepreviouspaneltostudythemean-revertingpropertiesofleverage
decisions.Inparticular,thespeedofmean-reversionofleverageisstillsubjecttogreat
debate in the literature[1]. I find that leverage mean-reverts to the long-run constant
level at a moderate speed of 35.87 percent per year. This estimate is close to the
empirical evidence of Flannery and Rangan (2006) and DeAngelo et al. (2011), who On the
suggest speeds of adjustmentof 34.40 and 37.80 percent per year, respectively. determinants
Fromaneconometricstandpoint,tothebestofmyknowledge,thisisthefirstpaperin
of firm
corporate finance that uses the EMM developed by Gallant and Tauchen (1996) to
leverage
estimate the model parameters. EMM is a systematic approach for selecting moments
when estimating a structural model using Generalized Method of Moments (i.e. the
researcherdoesnotneedtochoosearbitrarymoments).Thekeyideaofthisapproachisto 181
matchthemomentsimpliedbythestructuralmodeltothemomentsimpliedbythedata.
EMMestimationcanberegardedasatwo-stageprocedure.Inthefirststage,Iuse
asemi-nonparametric(SNP)densityfunctiontodescribethestatisticalpropertiesofthe
data,namely,investmentandleveragedecisions.Theoutcomeofthisstageisafamily
ofdensityfunctionsforthejointdistributionofthedata,andIchoosetheonethatbest
fitsthesampleinthemostparsimoniousway.Irecoverthestructuralparametersofthe
dynamic model in the second stage. These estimators are those that generate
T) simulationsofinvestment andleveragedecisionsascloseaspossibletotheobserved
P
5 ( data.Theestimatesofthestructuralparametersareconsistentwiththefindingsinthe
1
20 previous literature, have the correct sign according to economic theory, and are
ay statisticallysignificant.
M
5 Overall, determining the optimal capital structure of a firm is a complex problem
2
4 that has challenged academics and practitioners for a long time. Understanding
5
8: leveragedecisionsisofgreatimportancenotonlyforfinancialmanagers,butalsofor
0
At investors,suchasbanks,debt-holders,equity-holders,andothercapitalproviders,who
n needtounderstandhowfirmsmakecapitalstructuredecisionsinordertoachievean
a
g
hi efficient allocation of funds. From a practical perspective, the results in this paper
c
Mi suggestthatthefundamentalcharacteristicsofthefirm(i.e.elasticityofcapital,capital
of depreciation rate, etc.) could be used by practitioners to infer the firm’s optimal
sity leverage,aswellasitsevolutionovertime.Forinstance,abankanalyzingapotential
er loantoafirmcouldestimatewhetherthefirmstillhasdebtcapacity,dependingonits
v
ni currentdebtandtheoptimalleverageinferredfromitsprimitivefeatures.Furthermore,
U
y thefindingthatthedebtratioismean-revertingcouldbeusedbythebanktopredict
b
d thefirm’slikely evolutionof leverage in the future.
e
d
a
o
wnl I. Literature review
Do Leveragedecisionshavebeenanalyzedextensivelyinthecorporatefinanceliterature.
For example, Titman and Wessels (1988) find that leverage is significantly related to
firm size, profitability, and the uniqueness of the firm’s line of business. Using
internationaldata,RajanandZingales(1995)reportthatthefactorsthataresignificant
leverage determinants for USfirms (e.g. profitability,market-to-book ratio, sales, etc.)
aresimilarlyimportantinotherdevelopedcountries.Inamorerecentstudy,Frankand
Goyal(2009)findthatprofitability,market-to-bookratio,andfirmsize,amongothers,
are the most reliable factors explaining capital structure decisions[2]. However,
Lemmonetal.(2008)challengethatliteraturesuggestingthattheexplanatorypowerof
thosedeterminantsisratherlimitedandthatmostofthevariationincapitalstructure
at the cross-sectional level is captured by firm-specific fixed effects, which proxy for
unobserved factors. This study complements the latter by using a dynamic model of
thefirmtobothconfirmtheirresultsandprovidesomeinsightsonthepossiblefactors
underlyingthe unobserved fixed effects.
Fromthemethodologicalperspective,thispaperisclosesttoHennessyandWhited
(2007),whouseadynamicmodelofthefirmtoestimatethemagnitudeofthecostsof
IJMF external financing. Hennessy and Whited (2005) also use adynamic model to explain
11,2 empiricalfindingsapparentlyinconsistentwiththestatictrade-offtheory.Myanalysis
complements those studies by both focussing on the structural causes of the
unobserved heterogeneity described by Lemmon et al. (2008) and using EMM to
estimatethe structural parameters.
The paper is organized as follows. Section II describes the model. In Section III, I
182 describethedatausedforestimation.IdiscusstheidentificationstrategyinSectionIV.
In Section V, I examine the EMM procedure and present the estimation results.
SectionVIanalyzesthepredictionsofthemodelaboutleveragedecisionsandpresents
the main results of thepaper. Section VIIconcludes.
II. The model
ThemethodologyIusetodevelopthemodelisdiscretetime,infinitehorizon,stochastic
dynamic programming. The objective of the firm is to maximize its value, which is
T)
P achieved by maximizing the expecteddiscounted sum of cash flows to investors.
5 ( Agentsarerisk-neutralandusetherisk-freerateofinterest,r,astheirdiscountrate.
1 f
0
2 Statevariableswithprimesindicatevaluesinthenextperiod,e.g.,next-periodprofits
ay arereferredasz′,whilestatevariableswithminussignsindicatevaluesintheprevious
M
5 period,e.g.,previous-periodprofitsarez−.Finally,currentvaluesofstatevariablesare
2
4 indicatedwith no sign, e.g., current-period profits are z.
5
8: Therearetwoendogenousstatevariables:capitalkanddebtd.Thecapitalofthefirm,k,
0
At isusedforproductionandcanvary(i.e.increaseordecrease)overtimebecauseofinvestment
an decisionsanddepreciation.Ineachperiod,capitaldepreciatesataconstantrateδW0.
g
hi Thedebtofthefirm,d,maturesinoneperiodandisrolledovereveryperiod.The
c
Mi total amount of debt can be increased or decreased over time according to the debt
of decisions.Thedebtcontractincludesapositivenetworthcovenantbywhichif,inany
y
sit period,thevalueofthefirmfallsbelowthenominalvalueofthedebt,thefirmgoesinto
ver bankruptcy and is liquidated. Therefore, thebond yield requiredby debt-holders will
Uni depend on the probability of bankruptcy (described indetail below.)
by There is one source of uncertainty that drives the optimal policies of the firm, the
ed profitabilityshock,z.Thisshockchangesthemarginalprofitabilityofcapital,making
d
oa itmoreorlessattractivetoinvest.Therefore,highrealizationsofzarefollowedbylarge
nl
w investmentdecisions,andviceversa.IassumestatevariablezfollowsanAR(1)process:
o
D
z0 ¼cþr zþe0 (1)
z
where 0oρ o1 and ε is an iid truncated normal random va(cid:1)riab(cid:3)le with mean 0 and
z
variances2.Therefore,ifεtakesvaluesinthecompactsetE ¼ e;e ,thenshockztakes
e (cid:1) (cid:3)
valuesinthecompactsetZ ¼ z;z withz ¼cþe=1(cid:2)r andz ¼cþe=1(cid:2)r .
z z
Theoperating profitsof thefirm,π(k,z),dependon thecapital inplace, k,and the
profitability shock, z,in thefollowing way:
pðk;zÞ¼zka (2)
where aAð0;1Þ. Equation (2) shows that the operating profit function is of the
Cobb-Douglas form with decreasing marginal profitability.
I assume issuing debt and equity is costly. This assumption incorporates
the direct evidence provided by Altinkilic and Hansen (2000) on the importance
of underwriter fees. Furthermore, they suggest that the costs of issuance are convex,
bothfordebtandequity.Consequently,Iassumetheexternalfinancecostfunctionis On the
linear-quadratic: determinants
" (cid:4) (cid:5) # " # of firm
(cid:4) (cid:5) xd 2 ðxeÞ2
c xd;xe ¼f ldxdþld þf lexeþle (3) leverage
i d 1 2 d e 1 2k(cid:2)d
where xd and xe are the two decision variables. The former refers to debt 183
reductions ((cid:2)) and increments (+) while the latter refers to equity payouts ((cid:2))
and issuances (+). Parameters ld and ld reflect the costs of issuing debt, while
1 2
parameters le and le reflect the costs of issuing equity. The indicator function
1 2
ϕ equals 1 if xdW0, and 0 otherwise. Similarly, the indicator function ϕ equals 1
d e
if xeW0, and 0 otherwise. This means that issuing capital is costly while reducing
itis not.
T) Corporate earnings are taxed at rate τc. Therefore, the firm’s net income is
P defined by:
15 ( (cid:1) (cid:4) (cid:5) (cid:3)
20 NI ¼ pðk;zÞ(cid:2)dk(cid:2)c xd;xe (cid:2)r ðk;d;k(cid:2);d(cid:2);z(cid:2)Þd ð1(cid:2)t Þ (4)
y i d c
a
M
25 where rd(k, d, k−, d−, z−) is the bond yield required by debt-holders during the last
4 period (describedin detail below.)
5
8: Finally, the internal cash flow of the firm is:
0
At (cid:1) (cid:4) (cid:5) (cid:3)
gan ICF ¼ pðk;zÞ(cid:2)dk(cid:2)ci xd;xe (cid:2)rdðk;d;k(cid:2);d(cid:2);z(cid:2)Þd ð1(cid:2)tcÞþdk (5)
hi
c
Mi and its utility ineach period, orcashflow to investors, is:
of (cid:4) (cid:5)
sity u k;d;z;k(cid:2);d(cid:2);z(cid:2);xd;xe ¼(cid:2)xdþrdðk;d;k(cid:2);d(cid:2);z(cid:2)Þd(cid:2)xe: (6)
er
niv This is the cash flow received (+) orprovided ((cid:2)) by firm investors in each period.
U
y I now define the transition functions and state space of the two endogenous state
b
d variables. The state equation of capital k satisfies the accounting cash-flow equation
e
d and is definedas:
a
o
nl
ow k0 ¼kð1(cid:2)dÞþICFþxdþxe: (7)
D
Equation(7)meansthat,everyperiod,thefirminvestsanamount(cid:1)equ(cid:3)altoICF+xd+xe.
The capital, k, of the firm takes values in the compact set K ¼ 0;k where k is the
maximum level of capital. Following Gomes (2001) and Hennessy and Whited (2005,
2007), I assumethat under the highest profitability shock,z, capital k satisfies:
(cid:4) (cid:5) (cid:4) (cid:5)
p k;z ð1(cid:2)t Þ(cid:2) dþr k¼0: (8)
c f
Intuitively,atcapitallevelk,after-taxoperatingprofitsjustcoverdepreciationandthe
opportunity cost of capital. Therefore, it is not economically profitable to accumulate
capital to alevel k4k:
Thetransitionfunction of debt d is defined as:
d0 ¼dþxd: (9)
(cid:1) (cid:3)
The variable dtakesvalues in the compact set D ¼ 0;k .
IJMF Thepreviousrestrictionsonthestatespaceofkanddbindthedecisionvariablesxd
11,2 and xe to a compact set. Specifically:
(cid:1) (cid:3) (cid:1) (cid:3)
xdA (cid:2)d;k(cid:2)d andxeA (cid:2)ðk(cid:2)dÞ;k(cid:2)ðk(cid:2)dÞ : (10)
As stated above, the objective of the firm is to maximize its value, which is achieved
bymaximizingtheexpecteddiscountedsumofcashflowstoinvestors.Therefore,the
184
maximization problem faced by the firm is:
1
v ¼supE1 (cid:4) (cid:5)y subjecttod ok (11)
0 t¼0 t t t t
xdt;xet 1þrf
whereν isthecurrentvalueofthefirm,Eistheexpectationgivencurrentinformation
0
(i.e. initial capitalstock, debt and profitability shock), and y is definedas:
t
(cid:4) (cid:5)
PT) y ¼u k;d ;z;k ;d ;z ;xd;xe ifv 4d
5 ( t t t t t(cid:2)1 t(cid:2)1 t(cid:2)1 t t t t (12)
201 yt ¼Lt;ytþ1 ¼ytþ2¼:::¼0 ifvtpdt
y
a
M where L is the liquidation value of the firm at moment t as described below by
25 Equationt (13). The interpretation of the maximization problem is as follows: every
54 period the firm must choose xd and xe in such a way that it maximizes the expected
8: t t
0 discountedsumofcashflowstoinvestors(thisreferstothefirstlineofEquation(12)).
At
n However,ifinanyperiodthevalueofthefirmfallsbelowthenominalvalueofthedebt,
ga itgoesintobankruptcywhileinvestorsreceiveitsliquidationvalueandzerothereafter
hi
c (this refers to the secondline of Equation(12)).
Mi
of The model assumes the debt is protected with a positive net worth covenant, and
y thusthebankruptcy-triggeringeventconsistsinthevalueofthefirmfallingbelowthe
ersit nominalvalueofthedebt.Inthatcase,thefirmgoesintobankruptcyandisliquidated.
niv Accordingly, the (liquidation) value of the firm that goes intobankruptcy is:
U
d by vðk;d;z;k(cid:2);d(cid:2);z(cid:2)Þ¼L¼½kð1(cid:2)dÞþICFb(cid:3)ð1(cid:2)xÞ (13)
e
ad where ICF ¼[π(k, z)−δk](1−τ)+δk is the internal cash flow in the period previous to
o b c
nl bankruptcy and ξ reflects the direct costs of bankruptcy. Intuitively, the liquidation
w
Do value of the firm is the realization into cash of total assets (depreciated capital plus
internalcashflow) minus the directcosts of bankruptcy.
In theeventof bankruptcy,the recovery amount accruing to debt claimants is:
(cid:6) (cid:7)
Rðk;d;zÞ¼minfL;dg¼min ½kð1(cid:2)dÞþICF (cid:3)ð1(cid:2)xÞ;d : (14)
b
Equation(14)meansthatthevalue accruing todebt-holders istheminimum between
the liquidation value of the firm and the nominal value of the debt. Accordingly, fair
pricing of debt requires the fulfillmentof the following equation:
h(cid:4) (cid:5) (cid:8) (cid:9)i (cid:4) (cid:5)
1
d0 ¼ 1(cid:2)f d0ð1þr Þþf R k0;d0;z0 F dz09k;d;z (15)
1þr b d b
f
where the indicator function ϕ equals 1 if the firm goes into bankruptcy, and 0
b
otherwise. This equation means that debt-holders require a bond yield, r , which
d
equatesthenominalvalueofthedebt(left-handside)totheexpecteddiscountedpayoff
of debt in the next period (right-hand side). If the firm avoids bankruptcy, the debt
payoff is the nominal value plus the promised yield, d′(1+r ). On the contrary, if the On the
d
firm does go into bankruptcy, the debt payoff is the recovery amount, R(k′, d′, z′). determinants
Furthermore,thebondyieldrequiredbydebtclaimantscanbesolvedforexplicitlyand
of firm
is given by:
leverage
R (cid:4) (cid:5) (cid:4) (cid:5)
(cid:4) (cid:5) 1þr (cid:2)1 f R k0;d0;z0 F dz09k;d;z
rd k0;d0;k;d;z ¼ f Rd0(cid:4)1(cid:2)bf (cid:5)F(cid:4)dz09k;d;z(cid:5) (cid:2)1: (16) 185
b
The last step to complete the dynamic model of the firm is to describe its recursive
formulation.Letv¼v(k,d,z,k−,d−,z−).Then,thevalueofthefirmthatdoesnotgointo
bankruptcy is given by the following Bellman equation:
n (cid:4) (cid:5) R h(cid:4) (cid:5) i (cid:4) (cid:5)o
v¼sup u k;d;z;k(cid:2);d(cid:2);z(cid:2);xd;xe þ 1 1(cid:2)f v0þf L0 F dz09k;d;z
T) xd;xe 1þrf b b
P
5 ( subject to d0ok0:
1
0
y 2 (17)
a
M
25 Thisvaluefunctionrepresentsthemaximizedvalueofthefirm,namely,themaximized
54 expected discounted sum of cash flows to investors.
08: TheimplementationofthemodelisdescribedintheAppendix.Finally,letβ¼1/(1+r ),
n At thenthecompletevectorofmodelparametersisðb;d;c;rz;se;a;ld1;ld2;le1;le2;tc;xÞ. f
a
g
hi
Mic III. Data
of The data used in this study are from the yearly Standard & Poor’s Compustat
sity industrial files. The sample includes all firms in the database and covers the period
er 1988-2009. To select the sample, I follow a procedure similar to that of Hennessy
v
ni and Whited (2007). I delete firm-year observations with missing or negative data.
U
y Furthermore,Iincludeinthesampleonlyfirmsthathaveatleasttwoconsecutiveyears
b
d ofdata.Finally,Iexcluderegulated,financialorpublicservicefirms,thatis,Iexclude
e
ad allfirmswhoseprimarySICcodeisbetween4,900and4,999,between6,000and6,999,
o
nl or greater than 9,000. After this procedure, the final sample includes 14,465 different
w
Do firms and 111,944 firm-year observations.
Datavariablesaredefinedinthefollowingway:capitalkisBookAssets–Totaland
debt d is Long-Term Debt – Total plus Debt in Current Liabilities – Total. For
estimationpurposes,Icomputethefollowingtwodecisionvariables:investmentratio,i,
and book leverage, l. Therefore,thesedecision variablesare computed as:
(cid:1) (cid:3)
k0(cid:2)kð1(cid:2)dÞ
i¼
kð1(cid:2)dÞ
(18)
l ¼d0:
k0
Table I shows summary statistics of the sample. I eliminate observations with
investment W200 percent to reduce the effect of extreme observations and eradicate
errors in the data[3]. Consistently with previous empirical evidence, the investment
ratio decision has a mean value of 11.58 percent per year, while the book leverage
decision hasamean value of 46.55percent.
IJMF IV. Identification
11,2 Idiscussthesourcesofidentificationofr¼ðd;c;rz;se;a;ld1;ld2;le1;le2;xÞ,thevectorof
structuralparametersofthemodelthatwillbeestimated.Toachieveidentificationof
thesetenmodelparameters,Iassumetheremainingtwoparametershavethefollowing
values:β¼0.98,τ ¼35percent.Thevalueofβimpliesarisk-freerateofinterest,r,of
c f
2.04percentperyear.Ifixthevalueofthetaxrate,τ,becauseitwasrelativelyconstant
c
186 during the period 1988-2009.
Firm decisions are simultaneous and interrelated, and all model parameters
will have some impact on them. However, I can use certain data moments to identify
model parameters. The mean of investment is informative about the capital
depreciation rate, δ. A larger depreciation rate should imply more investment on
average. Variability of firm investment is informative about the concavity of the
profit function parameter, α. The lower the parameter, the lower the marginal
profitability of the firm, which means that firm investment should respond less
T) aggressively to profitability shocks.
P
5 ( The relative size of debt and equity issuances helps me identify the cost
1
ay 20 oisfsuisisnugindgebdtebcot,mlpd1aarneddtlod2,eaqnuditythsehcoousldt oinfdisuscueinrgelaetqivueitlyy,llae1rgaenrdislse2u.aLnacregseorfceoqstusitoyf,
M
5 andviceversa.Thevariabilityofdebtandequityissuancesalsohelpsmetopindown
54 2 parametersld2 andle2.Thelowerthequadraticparameters,thelessconvexthecostof
8: external capital function of the firm, which means that debt and equity issuances
0
At should be larger for a given profitability shock. The average level of firm leverage is
n informativeofthedirectcostsofbankruptcy,ξ.Higheraveragelevelsofleverageimply
a
g
hi lower direct costs of bankruptcy. Finally, because leverage is a relatively linear
c
Mi function of the profit shock, I can use the variation of leverage decisions (e.g. its
of persistence and variability) plus the parametric assumptions about the profitability
sity shock (i.e. state variable z follows an AR(1) process) to identify the remaining three
ver parameters of the process,c, ρz, and σε.
ni
U
y
d b V. Estimation
de Thissectionpresentstheestimatesofthestructuralparametersofthedynamicmodel.
a
nlo TheestimationtechniqueIuseistheEMMdevelopedbyGallantandTauchen(1996).
w
o The underlying idea of the methodology is to match the moments generated by the
D
simulationof themodel to those implied by the observeddata.
EMMestimationconsistsoftwosteps.Inthefirststep,Icharacterizethestatistical
properties of the data and select the density function that best fits the sample. In the
second step, I recover the structural parametersof the dynamic model.
Variable Mean Median SD Min Max Skewness Kurtosis
Investmentratio 0.1158 0.0563 0.3687 −0.9977 1.9998 1.6105 8.0830
Bookleverage 0.4655 0.4707 0.2301 0.0000 1.0000 0.0629 2.2226
No.observations 109,049
Notes: The sample consists of all firms in the Compustat database from 1988 to 2009, except
TableI. regulated,financialorpublicservicefirms.Thetablepresentsthemean,median,standarddeviation,
Summarystatistics minimum and maximum values, skewness, and kurtosis of investment and leverage in the final
ofthesample sample.Investmentratiois[k′−k(1−δ)]/[k(1−δ)],whilebookleverageisd′/k′
A. Description of the statisticalproperties of the data On the
IusetheSNPdensityfunction,asproposedbyGallantandTauchen(1989),todescribe determinants
the statistical features of the data (i.e. investment and leverage decisions). The SNP
of firm
densityisageneral-purposemodelwithwhichIgenerateafamilyofdensityfunctions
leverage
for the joint distribution of the data. I then select the density function that best
characterizes the data inthe most parsimonious way.
IfindthattheSNPdensityfunctionthatbestfitsthesampleofinvestmentandleverage 187
decisionsisabivariatenormaldensityfunctionwithaVAR(1)structureforthemeanand
an ARCH(3) structure for the variance. The description of the construction of the SNP
densityfunctionforthepresentstudyisavailableonmywebpage[4].
B. Estimation of structural parameters
Theobjectiveofthissecondstepistoestimatethevectorofparametersofthedynamic
T) model, r¼ðd;c;rz;se;a;ld1;ld2;le1;le2;xÞ. From the previous step, I have the SNP
P density that best characterizes the data. The score function of this density is used to
5 ( constructthevectorofmomentsthatwillbeusedintheGMMobjectivefunction.For
1
0
2 a candidate set of parameter values, I simulate the model and compute the objective
y
Ma function.Then,byusinganon-linearoptimizer,Isearchfortheparametervaluesthat
5 minimize the GMM criterion.
2
4 After simulatingthedecisionsofthefirm,themomentequationsarecomputedas:
5
8:
n At 0 m(cid:8)r;ey (cid:9)¼ 1 XN @logf(cid:8)y^ 9x^ ;ey (cid:9) (19)
ga n N @y t t(cid:2)1 n
hi t¼1
c
of Mi where fy^tgNt¼1 are the simulated data, N is the length of the simulation, and eyn is
y thequasi-maximumlikelihoodestimateoftheparametervector,θ,oftheSNPdensity
ersit function selected inthe first step.
v
ni TheEMM estimator is:
U
y (cid:8) (cid:9)(cid:8) (cid:9) (cid:8) (cid:9)
aded b r^n ¼argmrin m r;eyn 0 eIn (cid:2)1m r;eyn (20)
ownlo with eI ¼1Pn h@ logf(cid:8)y9x ;ey (cid:9)ih@ logf(cid:8)y9x ;ey (cid:9)i0, where the weighting
D n n t¼1 @y t t(cid:2)1 n @y t t(cid:2)1 n
e
matrix I assumes theSNP densityfunctioncloselyapproximatesthetruestochastic
n
process of y.
t
Under standard regularity conditions, the EMM estimator is consistent and
asymptoticallynormal.IftheSNPdensitycloselyapproximatesthetruedatagenerating
process, then the efficiency of the EMM estimator will be close to that of maximum
likelihood.
Foreachpossiblesetofparametervalues,thesimulationlengthis100,000 periods
after discarding the first 200 periods to avoid the influence of starting values.
As before, I assume β¼0.98 and τ ¼35 percent. Therefore, the vector of model
c
parameters to estimate is r¼ðd;c;rz;se;a;ld1;ld2;le1;le2;xÞ. Table II exhibits EMM
point estimates of model parameters, standard errors and p-values. All estimated
parametersare statistically significant, assuggested by thesmall p-values.
The estimate of the depreciation parameter, δ, at 0.073 per year is a reasonable
valueconsideringthatthemeaninvestmentratio,showninTableI,is0.116peryear.
Theestimateofthepersistenceparameteroftheprofitabilityshockprocess,ρ,is0.672.
z
IJMF
Parameter Estimate SE p-value
11,2
δ 0.0733 0.0009 0.0000*
c 0.5272 0.0097 0.0000*
ρ 0.6719 0.0286 0.0000*
z
σε 0.3908 0.0134 0.0000*
α 0.6244 0.0232 0.0000*
188
λd 0.0091 0.0004 0.0000*
1
λd 0.0004 0.0001 0.0012*
2
λe 0.0951 0.0043 0.0000*
1
λe 0.0049 0.0017 0.0019*
2
ξ 0.1412 0.0282 0.0000*
Notes: The sample consists of all firms in the Compustat database from 1988 to 2009, except
regulated,financialorpublicservicefirms.ThetablepresentsEfficientMethodofMoments(EMM)
estimates, standard errors, and p-values of model parameters. These parameters are: the capital
T) depreciation rate (δ), the constant coefficient of the profitability shock process (c), the persistence
015 (P TEMabMleeIsIt.imatesof ppraorcaemseste(σrεo),ftthheecpornocfiatvabitiylitoyfpthroecoespser(aρtzi)n,gthpercoofnitdfiutinocntaiolnsta(αn)d,athrdedcoevstisatoiofnisosfutihnegpdreobfitta(lbd1il,itlyd2s)haoncdk
y 2 modelparameters equity(le1 ,le2 ),andthedirectcostsofbankruptcy(ξ).*Statisticalsignificanceatthe1percentlevel
a
M
5
2
54 This value is similar to that reported by Hennessy andWhited(2007). The estimated
At 08: vwahluicehfisorsltighhetlcyonadbiotvioentahlesvtaalnudeaersdtimdeavtieadtiboynDoefAthnegeploroeftitaalb.(i2li0ty11s).hIofcinkd, σpεa,riasm0e.t3e9r1c,
n
a tobe0.527,whichimpliesthattheunconditionalmeanofprofitabilityshockispositive
g
Michi (givTehnethesattimρzatiseaolfsothpeopsaitriavme).eter related to the concavity of the profit function, α, is
y of 0.624 – consistent with the value found by Cooper and Haltiwanger (2006), Hennessy
sit and Whited (2007), and DeAngelo et al. (2011). Debt cost parameters ld and ld are
ver estimated at 0.009 and 0.0004, respectively, while equity cost paramete1rs le an2d le
ni 1 2
U estimatedat0.095and0.005,respectively.Thesevaluesareclosetothosereportedby
y
b AltinkilicandHansen(2000),HennessyandWhited(2007),andDeAngeloetal.(2011).
ed Finally, the estimated value of the direct costs of bankruptcy parameter, ξ, is 0.141,
d
a
o whichis slightlyabove that reported by Hennessy and Whited (2007).
nl
w
o
D
VI. Model predictionsabout capitalstructure choice
Theidentificationofthedeterminantsofcapitalstructureisastronglycontestedarea
incorporatefinance.Partoftheliterature(e.g.TitmanandWessels(1988);Rajanand
Zingales (1995); Frank and Goyal (2009), etc.) suggests that variation in capital
structure is explained by time-varying firm characteristics, such as profitability and
growthopportunities.Ontheotherhand,Lemmonetal.(2008)suggestthattheroleof
thosefactorsinthedeterminationofleverageisfairlylimitedand,therefore,important
factorsaremissinginexistingregressions.Iusethedynamicmodeltoinvestigatethese
issuesinthefollowingsubsections.Inagreementwiththelatter,Ifindthatmostofthe
variationinleverageisexplainedbythefundamentalcharacteristicsofthefirmandthe
power of traditionaldeterminants to explain such variation is rather small.
A. Features of the model
Ineveryperiod,thefirmmaximizesitsvaluebychoosingoptimalcapitalandleverage
depending on the current state of the model. The result of this behavior is shown in