testing theories of capital structure and estimating the

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Testing Theories of Capital Structure andEstimating the Speed of AdjustmentRongbing HuangKennesaw State University, [email protected]

Jay R. RitterUniversity of Florida

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Recommended CitationRongbing, Huang, and Jay R. Ritter. "Testing Theories of Capital Structure and Estimating the Speed of Adjustment." Journal ofFinancial & Quantitative Analysis 44.2 (2009): 237-271.

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JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS Vol. 44, No. 2, Apr. 2009, pp. 237-271COPYRIGHT 2009. MICHAEL G FOSTER SCHOOL OF BUSINESS, UNIVERSITY OF WASHINGTON, SEATTLE, WA 98195doi : 10.1017/S0022109009090152

Testing Theories of Capital Structure andEstimating the Speed of Adjustment

Rongbing Huang and Jay R, Ritter*

Abstract

This paper examines time-series patterns of externa! financing decisions and shows thatpublicly traded U.S, firms fund a much larger proportion of their financing deficit withexternal equity when the cost of equity capital is low. The historical values of the cost ofequity capital have long-lasting effects on fimis" capital structures through their influenceon firms' historical financing decisions. We also introduce a new econometric techniqueIn deal with biases in estimates of the speed of adjustment toward target leverage. We findlliat firms adjust toward target leverage at a moderate speed, with a half-life of 3.7 yearslor btwk leverage, even after controlling for the traditional dctenninants of capital structureand firm tixed effects.

I. Introduction

The three preetninent theories of capital sttitcture are the static trade-oif,

|)ecking order, and tnarket timing models. Other studies have examined the rela-

live merits of static trade-off and pecking order theories. In this paper we present

empirical evidence regarding the relative importance of all three of these hypothe-

ses. Using a direct measure of the equity risk premium (ERP), we find that U.S.

firms during 1964-2001 are much more likely to use external equity financing

when the relative cost of equity is low. Furthermore, ERPs have long-lived effects

on capital structure through their influence on securities issuance decisions, even

•Hu:ing, [email protected]. Coles School of Business. Kennesaw Slale University. 1000Chaslain Road NW. Kennesaw. GA 30144; [email protected], Wamngton College of Bu.si-ness Administration, tJniversily of Florida, PO Box 117168, Gainesville. FL 32611, We thank Chun-rong Ai. Hdny DeAngelo. Ralf Elsas, Kristine Hankiti.s. Steve Huddart, Marcin Kacperczyk. JaMinKarceski, Robert Kieschnick, Paul Malatesta (the editor). Andy Naranjo. M. Nimalendran, GabrielRamirez. Kasturi Rangan, Michael Roberts. René Stulz. Jeffrey Wurgler, ttonghang Zhang, and espe-cially Mark Flannery and Ivo Welch, and seminar participants at Ihe University of Florida, KennesawState University, the University of Michigan, NTU (Singapore), the 2004 All-Georgia Finance Con-ference at the Federal Reserve Bank of Atlanta, the October 2(X)4 Notre Dame Behavioral FinanceConference, the 2(X)5 Western Finance Association Conference, and the 2005 Financial ManagementAssociation Conference, as well as two anonymous referees for useful comments. We also ihankViUhan Goyal. Kamil Tahmiscioglu. and Richard Warr for kind programming assistance and XiaoHuang for help with econometrics. This paper is based on Ronghing Huang's 20()4 University ofFlorida doctoral dissertation. Eariier versions of this paper were circulated under the lille "TeslingIhe Market Timing Theory of Capital Structure." but most of the analysis on the speed of adjustment(Section V) was added subsequently.

237

238 Journal of Financial and Quantitative Analysis

after controlling for the traditional determinants of capital structure, consisteniwith the hypothesis that market timing is an important determinant of observedcapital structures, After further controlling for firm fixed effects and correctingfor biases that are created by some of the firms being present for only a .short panof the sample period and leverage ratios being highly persistent, we find that firmsadjust toward their target leverage at a moderate speed.

No single theory of capital structure is capable of explaining all of the time-series and cross-sectional patterns that have been documented. The relative impor-tance of these explanations has varied in different studies. In general, the peckingorder theory enjoyed a period of ascendancy in the 1990s, but it has recentlyfallen on hard times. With the publication of Baker and Wurgler's (2002) articlerelating capital structure to past market-to-book ratios, the market timing theor\has increasingly challenged both ihe static trade-off and pecking order iheories,A number of recent papers, however, challenge Baker and Wurgler's evidence thaisecurities issued in a year have long-lived effects on capital structure.

The market timing theory posits that corporate executives issue securities de-pending on the time-varying relative costs of equity and debt, and these issuancedecisions have long-lasting effects on capital structure because the observed cap-ital structure at date / is the outcome of prior period-by-period securities issuancedecisions. According to the market timing theory, firms prefer equity when theyperceive the relative cost of equity as low. and they prefer debt otherwise. Thecapital structure literature has. to date, refrained from explicitly measuring thecost of equity. A major contribution of this paper is to link securities issuanceexplicitly to the cost of equity capital, using a direct measure of the ERR

Shyam-Sunder and Myers (1999) lest the pecking order theory by estimatingan ordinary least squares (OLS) regression using a firm's net debt issuance as thedependent variable and its net financing deficit as the independent variable. The\find that the estimated coefficient on (he financing deficit is close to one for theitsample of 157 firms continuously listed during 1971-1989, and they interpret theevidence as supportive of the pecking order theory. Frank and Goyal (2(X)3). how-ever, find that the coefficient on the financing deficit is far below one in the 1990s.We explore the role of changing market conditions in firms' changing financingbebavior. We find that our market condition proxies, especially a measure for thetime-varying cost of equity capital, have an important impact on the estimatedcoefficient of the financing deficit.

To measure the relative cost of equity, we use the beginning-of-year impliedHRP, estimated using forecasted earnings and long-term growth (LTG) rates. Con-sistent with the market fiming theory, we find that firms fund a large proportionof their financing deficit with external equity when the relative cost of equity islow. The magnitude of the effect is economically and statistically significant. Forexample, an increase from 3% to 4% in the implied ERP results in approximately3% more (e.g., from 62% to 65%) of the financing deficit being funded with netdebt. To our knowledge, our study is the first to systematically link the time seriesof financing choices to the time-varying ERP for a large sample of U.S. publiclytraded firms.

After establishing the importance of market conditions for securities issuance,we examine the effect of historical ERFs on current leverage. We find that past

Huang and Ritter 239

ERPs have long-lasting effects on a firm's current capital structure through theirinfluence on historical financing decisions. A firm funds a larger proportion ofits financing deficit with debt when the market ERP is higher, resulting in higherleverage for many subsequent years. For example, a financing deficit that was

of total assets in 1974, when the ERP was high, results in an increase ofin hook leverage {e.g.. increasing from 47.09% to 50%) four years later,

while a financing deficit of 10% in 1996, when the ERP was low, results in anincrease of only 0.35% in book leverage four years later.

We also estimate the speed with which firms adjust toward target leverage.This is perhaps the most important issue in capital structure research today. Iffirms adjust quickly toward their target leverage, which changes across time asiirm characteristics and market conditions change, then historical financing ac-tivities and market conditions will have only short-lived effects on firms' currentcapital structures, implying that the market timing theory of capital structure isunimportant.

The existing literature has provided mixed results on the speed of adjust-ment (SOA) toward target financial leverage. Fama and French (2002) estimatean SOA of 7%-18% per year. Lemmon, Roberts, and Zender (2008) find thatcapital structure is so persistent thai the cross-sectional distribution of leveragein the year prior to the initial public offering (IPO) predicts leverage 20 yearslater, yet they estimate a relatively rapid SOA of 25% per year for book leverage.Flannery and Rangan (2006) estimate an even faster SOA: 35.5% per year usingmarket leverage and 34.2% per year using book leverage, suggesting that it takesabout 1.6 years for a firm to remove half of the effect of a shock on its leverage.Both Lcary and Roberts (2005) and Alti (2006) find that the effect of equity is-suance on leverage completely vanishes within two to four years, suggesting fastadjustment toward target leverage. As Frank and Goyal (2008) state in their sur-vey article; "Corporate leverage is mean reverting at the firm level. The speed atwhich this happens is not a settled issue" (p. 185).

We reconcile these different findings by showing that the estimated SOAin a dynamic panel model with firm fixed effects is sensitive to the econometricprocedure employed when many of the firms are present for relatively brief pe-riods, especially when a firm's debt ratio is highly autocorrelated. A traditionalestimator for a dynamic panel model with firm fixed effects involves mean dif-ferencing the model. As Flannery and Rangan (2006) observe, however, the biasin the mean differencing estimate of the SOA can be substantial for a dynamicpanel data set in which many firms have only a few years of data (the short timedimension bias). To reduce the bias. Flannery and Rangan (2006) rely on an in-strumental variable in their mean differencing estimation, while Antoniou, Guney,and Paudyal (2008) and Lemmon et al. (2008) use a system generalized method ofmoments (GMM) estimator. In the system GMM estimation, the model itself andthe first difference of the model are estimated as a "system." The system GMMestimator, however, is hiased when the dependent variable is highly persistent, asis the case with debt ratios.

Hahn, Hausman, and Kuersteiner (2007) propose a long differencing estima-tor for highly persistent data series. In this estimator, a muitiyear différence ofthe model is taken rather than a one-year difference. Our simulations show that


the long differencing estimate is much less biased than the OLS estimate ignoringfirm fixed effects unless the true SOA is slow, in which case neither procedurehas an appreciable bias. The long differencing estimate is also much less biasedthan ihe ñrm fixed effects mean differencing estimate unless the true SOA is fast,in which case neither procedure has an appreciable bias. Hahn et al. (2007) show-that the long differencing estimator is also much less biased than the system GMMestimator when the dependent variable is highly persistent (i.e., the true SOA isslow). In ¡I simulation, they show that if the true autoregressive parameter is 0.9.the system GMM estimate is only 0.664. whereas the long differencing estimatorproduces an estimate of 0.902 with a differencing length of k = 5.

Using the long differencing technique, we find that firms only slowly rebal-ance away tbe undesired effects of leverage shocks. Using a differencing lengthi)f A: = 8, the SOA is 17.0% per year for book leverage and 23.2% per year formarket leverage. Such estimates suggest that it takes about 3.7 and 2.6 years fora firm to remove half of the effect of a shock on its book and market leverage,respectively. This is the most important result of this paper.

Throughout our empirical analysis, we do not give equal attention to the mar-ket timing, pecking order, and static trade-off models. This is because many of ourfindings are consistent with earlier research, and little purpose would be senedby long discussions that would largely repeat the existing literature. Instead, wefocus on our new findings regarding time variation in the relative cost of equityas it relates to the pecking order and market timing hypotheses, on whether pastsecurities issues have persistent effects on capital structure, and on the SOA totarget leverage.

The rest of this paper is organized as follows. Section [I describes the dataand summary statistics. Section III presents the empirical results of the roie ofmarket timing in securities issuance decisions. Section IV examines the effects ofsecurities issues on capital structure. Section V discusses econometric issues andpresents estimates of the SOA to target capital structure using the long differenc-ing estimator. Section VI concludes.

II. Data and Summary Statistics

A. Data

The firm-level data are from the Center for Research in Security Prices(CRSP) and Compustat. The sample consists of firms from 1963 to 2001. SinceR&D (item 46) is missing for about 39% of firm years, we set tbe missing value tozero to avoid losing many observations. We rely on a dummy variable to captureihe effect of missing values when using R&D in our analysis.' Utilities (4900-4949) and financial firms (6000-6999) are excluded because they were regulatedduring most of the sample period. A small number of firms with a format code

'The vast majority of firms with missing R&D are in indtjstncs stich as clothing retailers forwhich R&D expenditures are likely lo be zero. Capilal expenditures and convenible debt are missingfor about 2% of firm years. We set missing capilal expendilures ( 128) and convertible debt (79) to zero.although our results are essentially the same if we exclude firm years with mi.ssing capital expendituresor convertible debt.


of 4, 5. or 6 are also excluded from the sample,^ Firm years with beginning-of-year book assets of less than $10 million, measured in terms of 1998 purchasingpower, are also excluded to eliminate very small Hrms and reduce the effect ofoutliers.' Finally, we exclude firm-year observations for which there was an ac-counting change for adoption of Statement of Financial Accounting Standards(SFAS) No. 94, which required firms to consolidate off-balance sheet financingsubsidiaries."*

B. Summary Statistics of Financing Activities

Summary statistics of financing activities are presented by year because weare interested in the time-series properties. Figure 1 presents financing activifiesusing information from the balance sheet. Net debt is defined as the change inbook debt. Net equity is defined as the change in book equity minus the changein retained earnings. Following Baker and Wurgler (2ÍX)2) and Fama and French(2002). book debt is defined as total liabilities plus preferred stock (10) minusdeferred taxes (35) and convertible debt (79), and book equity is total assets lessbook debt,^

In Figure 1, the average ratios are the annual averages of net financing scaledby beginning-of-year assets (in percent), and the aggregate ratios are the annualaggregate amount of net financing of all firms scaled by tbe aggregate amountof beginning-of-year total assets (in percent). Figure 1 shows tbat the averagenet debt increase exceeded 10% of beginning-of-year assets in eight years. Theaverage net equity issuance exceeded 6% in 12 years. The average change inretained earnings shows a declining trend, witb tbe lowest value in 2001. tbe lastyear of our sample period. Tbe aggregate net debt and equity issuances fiuctuatesubstantially, witb aggregate net external equity issuance peaking at over 7% ofaggregate assets in 2000. The static trade-off theory has been unable to providea satisfactory explanation for the magnitude of tbese fiuctuations. The pecking

•Format code 5 is for Canadian hrms, and format codes 4 and 6 are noi delincd in Compustat.To further reduce the effect of outliers, we also drop lirm-year observations with book leverage

or market leverage that is negative or greater than one and Tobin's Q that is negative or greater ihan 10.These variables witi be defined later. Our results are robust to whether or not we keep these firm-yearobservations.

" We exclude 20! such lirm years identified with Compustai footnote codes. The Financial Ac-i ounting Standards Board (FASB) issued SFAS No. 94 in late 1^87. Heavy equipment manufacturers,ind merchandise reiailers were most affeeted by the standard because they made extensive use ofLinconsolidated finance subsidiaries. For example. Ford. General Motors. General Eiectriu. and Inter-iiaiional Business Machines all had a huge increa.se in debt on iheir balance sheels from liscal year1987 to I yXH. More specifically. Ford had a debt increase of about $93.8 billion, while its end-of-yearlolal assets were $45.0 billion in 1987 and $I4.Î.4 billion in 1988. largely because Ford Credit wasconsolidated under the new standard. This standard also caused some firms lo divest themselves ofunconsolidated subsidiaries because otherwise they would violate debt covenant agreements on themaximum amount of leverage, and their returns on assets would appear too low and financial leveragewould appear too high.

• When ihe liquidating value of preferred stock (item tO) is missing, we use the redemption valueof preferred st(K-k (56). When the redemption value is also missing, we use ihe carrying value of pre-lerred stock (130). As one referee noted, convertible preferred stock is more equity-like than straightpreferred slock. In iinreported analysis we include the change in ihe carrying value of convertiblepreferred slock (2t4) in our definition of net equity. Our results remain qualitatively ihe same.

242 Journal of Finanoial and Quantitative Analysis

FIGURE 1

Average and Aggregate Financing Activities from the Balance Sheet

Net debt is the change in debí and preferred stock (Compustat items 181 + 10 - 35 - 79). Net equity is the change inequity anO convertible debt (items 6 - 181 — 10+ 35 +79) minus the change in retained earnings (36). Graph A of Figufe 1Sfiows the equally weigtiied annual averages of net financing scaled by beginning-of-year assets ol each firm (in percent)Graph B shows the annual aggregate amount of net financing of all (irms in Ihe sample scaled by the aggregate amountof beginn in g-of-year assets (in percent).

Graph A. Equally Weighted Averages ol Net FinanCing/Assels

25

20

15

1 0 •

-5

-10-

-15

Average Nel Debt

Average Met Equity

Average Change in Retained Earnings

Year

Graph B. Aggregate .Amount of Net Financing/Aggregate Amount of Assets

12 •

10 -

' Aggregate Net Debt

Aggregate Net Equity

Aggregaie Change in Reialoed Earnings

YMT

order theory gains some support during 1974-1978, when the average net equityissuance was below 2%. As so often happens, however, the pattern on whichthe pecking order hypothesis was based began to break down shortly after thepublication of Myers (1984).

Figure 1 understates securities issues because other firms that are retiringdebt or buying back stock lower the averages. Table 1 reports the percentage offirms that are net securities issuers. Issuing firms in a year are defined as those for


TABLE 1

Percent of Firms in Different Financing Groups across Time

A firm is defined as issuing debt if AD scaled by beginning-of-year assets is ai leasi 5%. where AD is the change in debland preferred stock (Compustat items 181 + 10 — 35 - 79) Iromyear í — 1 to year (. or issuing equity if AE scaled bybeginning-of year assets is ai least 5%, where AE is tfie change in equity and convertible debl (6 — 181 — 10 + 35 + 79)minus the change in retameö earnings [36). The percentages of debt and equity issuers do not necessarily add up to 100because firms can issue both debt and equity or neither debt nor equity. Firms wilh beg inn in g .-of-year assets of iess than$10 million (1998 purchasing power) are excluded.

Year Total Number of Firms Debt Issues (%) Equity Issues (%)

1963196419651966196719681969197019711972197319741975197619771978197919801981198219831984198519861987198819891990199119921993199419951996199719981999?000youi

129465558722

1.3161,5701,9292,2112,4932,7392,9863,0393,0973.0462,9862.8752,9052.9752.9153,0733,0653,1463,2103,0793.1043,0973,0753,0633,0413,1333,3803,7153.9444.2144,5434,5644.3664,2024.160

33.335.745.954,243.853.947.440.933.843.058.657.928.138.646957 756.945.542.434.835.745.340.239,643.944 441 239.730,635.840.245.047.643.544.849.544 743.128.4

16.312.014.316.316.624.534.114.714 416.710.46.8668.1799.511.615.419.313.123.117716.419.419.614.814.713.516.221 824.024 525 229.729.527.426.731.527.7

which debt or equity Increases by more than 5% of beginning-of-year assets, thesame definition that has been used, for example, in Hovakimian, Hovakimian, andTehranian (2004) and Korajczyk and Levy (2003). Once we separate firms withnet securities issues from other firms, we see a higher frequency of issuing. Thepercentage of firms with net debt issuance of at least 5% of assets is never below28%. The pecking order theory predicts that equity issues will be rare. However,the proportion of net equity issuers (firms issuing at least 5% of assets) neverdrops below 6.6% in any year, peaks at over 34% in 1969, and is at least 25% ineach year from 1995 to 2001.^

""Our proportion of equily issuers is much higher than in studies such as Jung. Kim. and Stul/.( 1996) and DeAiigelo. DeAngek), and Stulz(20O9}, which define an equily issuer as a lirm conductinga public seasoned equity offering for cash. Our definition of an equity issuer, which is standard inthe empiricaJ capital structure literaiure. includes firms that conduct private placements of equity orstock-financed acquisitions that increase the book value of equity by at least 5% of assets, net of sharerepurchases.


Overall, our summary statistics of financing activities cast doubt on the abil-ity of the pecking order model to describe most of the observed capital structures,consistent with Fama and French (2002), (2005), Frank and Goyal (2003), andHovakimian (2006).

C. Summary Statistics of Macroeconomic Variables

How do firms judge the relative cost of equity? On the one hand, some firmexecutives may possess private information that is not reflected in market pricesabout their firms or their industries. On the other hand, they may follow certainpsychological patterns. For example, reference points, as suggested by prospecttheory, may play a role.^ Alternatively, they may issue equity to take advantageof publicly observable misvaluations if the equity market becomes temporarilyovervalued (Stein (1996)).

Our proxy for the cost of equity is the implied ERP, estimated using analystearnings forecasts (earnings per share (EPS) and LTG rate) at the end of the pre-vious calendar year for the 30 stocks in the Dow Jones Industrial Average.** Theimplied ERP is defined as the real internal rate of return that equates the currentstock price to the present value of all future cash flows to common sharehold-ers of the firm (measured as book value of equity plus forecasted future residualearnings), minus the real risk-free rate (see Appendix A for details). Althoughthey differ in their specific procedures, this is the general approach used by Clausand Thomas (2001), Gebhardt, Lee. and Swaminathan (2001). and Ritter andWarr (2002).'' We follow Ritter and Warr (2002) to correct for inflation-induceddistortions in the estimation of the implied ERP. The equally weighted average of

^Casual conversations with investment bankers suggest thai when they advise their clients onthe choice beiween debt and exiernal equity ñiiancing. the most imptmani factors they consider tirt-whether a client's sttKk ptice is near a 52-week high and whether the earnings yield on the stock ishclow the interest rate on debt.

' By using the lagged year-end values during year / lor a firm with a Dec. 31 fiscal year, we arcusing the Dec. i I of year / ~ I accounting information and sttKk price. For a firm with a June 30fiscal year, during year i we use the June 30 of year i - 1 accounting information and Dec. 31 of year/ - 1 stCMjk price. We use forecasts from Value Line for 1968-1976 and from Institutional Brokers"Estimate System (IBES) for 1977-2001. We hand-collect Value Line data from Value Line ¡nvestmcriiSiin-ey for early years when the IBES database is not available. Because previous studies documentthat IBES and Value Line analysts make systematically dilïereiit forecasts, we estimate the impliedERP for 1977 usitig analyst Ibreca.sts from hoth sources and then adjust the implied ERP for 1968-1976 by multiplying the Value Line forecast by the ralioof the 1977 premium using IBES to the 1977premium using Value Line. Brav. Lehavy, and Michaely ( 2()0,'i I estimate the implied nominal expectedmarket return using target prices and future dividends from Value Line for 1975-2001. They estimateannual nominal expected returns varying from 34.1'Ä: in 1975 to 12.1'^ in 1997, Using their seriesinstead of ours dt>es not change our major results. Our qualitative results are also robust to using theval tie-weighted bo(»k-to-market ratio of equity for all NYSE-listed firms as a proxy for the relativecost of equity rather than the implied ERP,

Consistent wiih the literature, we assume that analyst EPS forecasts are exogenous. Bayesian ;iii-alysts, however, may become overly conservative in their forecasts of EPS when the cost of equity ishigh, and overly optimistic when the cost of equity is low. This is because the market price implies fu-ture earnings, and a Bayesian analyst will incorporate these into his or her own forecasts. Funhermore.when P/E ratios are high, more optimistic forecasts are necessary in order to jastify "buy" recommen-dations. The endogeneity results in a dampening of the time series of the implied ERP relative to itstrue fluctuations and hence creates a bias against our results.


the implied ERP for each of the Dow 30 stocks is u,sed as an estimate of the ERPfor the market. The time-variation of the implied ERP may be due to either thetime-variation of risk, or of the risk aversion of investors (rational reasons), or tothe time-variation of investor sentiment (an irrational reason).

Figure 2 shows the real interest rate (RIR) and the implied ERP at the end ofeach calendar year. The HRP turned negative during 1996-2001. suggesting over-valuation of the stock market.'" Firms display a high propensity to issue equityduring these years, as indicated in Table 1.

FIGURE 2

Equity Risk Premium and Real Interest Rate

The market equity risk premium is estimated using analyst forecasts at the year-enö for ttie Dow 30 stocks from Value Linetor 1968-1976 and from IBES for 1977-2001. The real interest rate is the nominal Interest rate minus inflation, whsre thenominal interest rate is the yield on one-year Treasury biiis in the secondary market at the beginning of each calendar yearat http://www. fed eral reserve.gov/, and inflation is the rate of change of the consumer pnce inöex during the calendar yearIrom CRSP.

Equity Risk Premium

Real Inierest Rate

Year

Figure 2 also shows that the RIR was very low in 1973-I974and 1978-1979,when the percentage of sample firms issuing debt rose to historic highs (over 56%

"'Although we eslimate a negative ERP for some years, our qualitative results are not dependenon Ihe ERPs being negative. The residual income methodology that we employ states thai the value ofequity is equal to the book value of equity plus the present value of future residual income (economicprofits). Because we assume that future residual income i.s mean-revening, a large present vahie offuture residual income can only be achieved by using a low discount rate (i.e., since the numeratorconverges to zero, a small denominator is needed to generate a high ratio). When both the market-to-book ratio and the RIR are high, as was the case in the 1996-2(X)I period, the mixlel produces anegative implieJ ERP. Some have argued that a high market-to-book ratio has existed in most yearsafter 1995 because the book value of equity increasingly underrepresents the value of assets in placeas intangibles represent more and more of firm value. 11* so, our estimates may overstate the downtrendin the ERP. and the true HRP may not be as negative as we estimate. Since we use ihe ERP as anexplanatory variable, overestimating its decline would lead to underestimating the slope coefficient onIhe ERP.

246 Journal of Financia! and Quantitative Analysis

for each of these years in Table 1 ). The RIR is used as a proxy for the lime-varyingcost of debt perceived by corporate executives.

Previous studies also use the term spread and the defauh spread as proxies forIhe costs of various forms of debt (e.g.. Baker, Greenwood, and Wurgler (2003)).It is likely that the time-varying default risk premium can help explain the time-varying financing decisions. We thus include the default spread, which is definedas the difference in yields between Moody's Baa- and Aaa-rated corporate bonds.The term spread, defined as the difference in yields between 10- and one-yearTreasuries, is also included because firms might increase the use of long-termdebt when the term spread is low.

We also include contemporaneous measures of the statutory corporate taxrate and the real gross domestic product (GDP) growth rate. The statutory cor-porate tax rate has changed over time and may have a major influence on thefinancing decisions of U.S. firms (see, among others, Graham (2003) and Kale,Noe, and Ramirez (1991))." The real GDP growth rate controls for growth op-portunities. To the degree that these variables are important and have the expectedsigns, this lends support to the static trade-off model.

The lagged average announcement effect on seasoned equity offerings (SEOs)is included to see whether, as implied by the pecking order theory, time-varyinginformation asymmetry is able to explain time-varying financing activities. Sincethe pecking order theory assumes that markets are semi-strong-form efficient, theannouncement eifect associated with equity issues is the primary proxy for thelevel of information asymmetry (Bayless and Chaplinsky (1996)).

Table 2 reports summary statistics for our proxies for market conditions.The implied ERP is positively correlated with the default spread and the statutorycorporate tax rate and is negatively correlated with the RIR.

III. Market Timing and Securities Issuance Decisions

How important are market conditions, especially the ERP, in securities is-suance decisions? This section reports and discusses the results from i) annualOLS regressions using a firm's net debt issuance as the dependent variable andits net financing deficit as the independent variable, ii) pooled OLS regressionslinking the pecking order slope coefficient to the time-varying cost of capital,and iii) a pooled nested logit regression for the joint decision of whether to issuesecurities and which security to issue.

A. Pecking Order TestsI

Following Shyam-Sunder and Myers (1999), we first estimate

(1)

"The statutory corporate tax rate was 52% in 1963, 50% in 1964, 48% in 1965-1967. 52.8% in1968-1969.49.2% in 1970.48% in 1971-1978.46% in 1979-1986.40% in 1987.34% in 1988-1992,and 35% in 1993-2001.


TABLE 2

Summary Statistics of Macroeconomic Variables

ERPi _ 1 is the implied market equity risk premium at the end ot year î - 1, eshmated using analyst forecasts for ihe Dow30 stocks from Value Line for 1968-1976 and from IBES for 1977-2001 RIR,_i is the nommai m lef es I rale minus realizedinflation, where the nominal interest rate is the yield (daily series) on one-year Treasury bilis m ttie secondary market at theend of year t — 1 al hltp:/Avww fade rai reserve.gov/. and inflation is the rale of change of the consumer price index duringyear f from CRSP. DSP, _ i is the default spread, defined as the difference in yieids (weskiy series. Since daily series onlygoes back to 1983) between f^ioody's Baa-rafed and Aaa-ialed corporate bonds al the end of year f - 1. TSP,_ t is Iheterm spread, defined as ihe difference in yields (daiiy series) between 10- and one-year constan! maturity Treasuries at theend of year / - 1. TAXR, is the statutory corporate lax rale during year t RGOPt is the reai GDP growth rate during yearf from tfie Bureau of Economic Analysis, Department of Commerce RSEO[_i is the annual average of mafket-adjustedreturns during year [ — I from one day before to one day after the fiie date of seasoned equity offerings (SEOs], computedby the authors using SEO data from Thomson Financial. The average announcement effect is caiculated from 1980. thefirst year the file date is available for most SEOs. SubscriQt f denotes the current year and I - 1 denotes the previous yearTAXR, RGDP, and RIR are available for 1963-2001 " " . "'. and " denote slatisticai significance al Ihe 1%, 5%. and 10%levéis, respectiveiy, in a two-tailed test

ERP,_, DSPr_, TSP,_, TAXR. RGDP,

NMeanStd DevMmMedianMax

CorrelaiionERPr-1RiR,_,DSP,_,TSP,^,TAXR,RGDP,RSEO,_ 1

330.0310 037

- 0 0430.0370.114

1-0.316-

0 469—-0.058

G.705—- 0 181

0.191

390.0160.027

-0,0540,0160,063

10.346"0.218

-0.257-0.035

0.259

390 0110.0050.0030.0090.02^

10,1170 126

- 0 376"0.422"

390 0070.011

-0.0140-0060,031

1-0.255

0.291-- 0 273

390.4300.0670.3400.4600,528

10.1580.420-

390.0330.022

-0,0200.0360.073

10.077

21-0.018

0.005-0.028-0.017-0.008

1

where ADu is the change in book debt as a percentage of beginning-of-year as-sets for firm / at the end of the fiscal year ending in calendar year t, and DEF,,is the change in assets minus the change in retained earnings as a percentage ofbeginning-of-year assets. To examine how the slope coefficient on the financingdeficit has changed across time, we estimate this equation each year. The esti-mated slope coefficient, b, known as the pecking order coefficient, shows veryinteresting time-series patterns and is reported in Figure 3. It ranges from 0.67 to0.92 in the 1960s and the 1970s, from 0.48 to 0.79 in the 1980s, and from 0.27to 0.58 from 1990 to 2(W) I. Frank and Goyal (2003) find that the slope coefficientwas low in the 1990s as well. However, a time trend does not explain everything.Even within each decade, there are ups and downs that might be explained withour proxy for the relative cost of equity capital.

Since the effect of market conditions on a negative financing deficit is un-clear, we focus on the effect of market conditions on a positive financing deficitby estimating the following regression, pooling all firm year observations:

(2) = a + /^NDEF,; + {c + Í /ERP,_ , + Î R Ï R , _ , +/DSP,_ i +

+ /ïTAXR, +jRGDP; + jtRSEO,_ i ) x PDEF,, + a,,

where NDEF,, equals DEF,, if DEF,, < 0 and zero otherwise; PDEF,, equalsDEFj, if DEF,f > 0 and zero otherwise: ERP,_ i is the implied market ERP at theend of y e a r / - !;RIR,_i is the expected real interest rate at the end of y e a r / - 1;DSP,_ I is the default spread at the end of year / - 1 : TSP,_ i is the term spreadat tlie end of year / - 1; TAXR, is the statutory corporate tax rate during year /;


FIGURE 3

Pecking Order Slope Coefficients

Coefficients a'e computeö annually by estimating Gquation ( 1 )

1.0 -

0 9 •

08 -

07 •

I 06 -Ü

I 05-D.

03 •

0.2 -

0 . 1 •

00

Year

RGDP, i.s the reai GDP growth rate during year /: and RSEO;_| is the annualaverage of market-adjusted returns for the three-day window [ - 1. -i-1 ] surroundingthe nie date of SEOs during year î — I (SKO data is from Thomson Financiarsnew issue-s database). The market timing theory predicts a positive coefficienton the interaction between the ERP and the positive financing deficit. Resultsare reported in Table 3. Correlation of the observations across time for a giventirm and correlation across firms for a given year could rcsuh in biased .standarderrors in our panel data set regressions. Consequently, we report /-statistics usingstandard cn'ors corrected for clustering by both firm and year (Petersen (20(19)).'-

Consisteni with the market timing theory, firms finance a large proportion ofiheir financing deficif with net external equity when the cost of equity is low\ InPanel .\ of Table 3. we follow Baker and Wurgler (2002) to define the financingdeficit as including dividends and the change in cash (i.e.. higher dividends in-crease the financing deficit). In regression ( 1 ), the implied ERP at the end of yearÍ — I is positively related to the pecking order coefficient in year !. \n economicterms, a one-standard-deviation (0.0371 increase in the implied ERP is associatedwith 10.8% more of the financing deficit being funded with net debt (for exam-ple, increasing from 60% to 70.8%). Elliott, Koeter-Kant, and Warr (2007) also

'•^Petersen (2009) suggcsis liial lin.' Rogers 11993) standard errors ciustered by firm and by yearare more accunitc than uncorrcclL'ci standard errors in the presence of hoth linn and year correlalionsin il panel data set. The existing STATA software does not have a built-in command lo corred Ibrtwo-dimensiona] clustering (lor fxample. clustering hy hoth firm and year). However. MitL-hell Pe-lersen kindly provides a ST.ATA ado tile used in Petersen (2íH)9) lor two-ditiien.sional ckisterinLi (seehttp://w ww.kellogg.northwestern.edu/faculty/potcrsen/htm/papcr.s/se/se.programminii.htm).


TABLE 3

Market Conditions and the Funding ot the Financing Deficit

""(ie fGlloÄ''ng equatiori is &i!imaiea

^0,1 = a + &NDEF,- + (c + dERPt_i - eRIR;_i t /DSP,_i +gTSP,- i + hTAXR,

» (RGDPi t «RSEO, - T ) X PDEF,, + £„ .

In Panel A ol Table 3. me financing defol DEF,,. is defined as Ji.D,i * JE,;, where AD,t is itie change in cJebt and preferredslock (Compuslatilems I8i + 1O - 35—79)iromyeaf ! - 1 loyeai ras a percentage otDegmning-of-year assets for firm i.;ind.ilE„ is ttie change in equity and convertible debi (items 6 - 181 - 10+35 + 79] minus the change m retained earningsi;item36)asapercentageofDeginning-of-vear assets. In Panel B. the financing deficit eicludes dividends (item 127) anarue change in cash (item 1 ;• in botn panels. NDEF,, equals DEE,, if the deficit is negative and zero otherwise, and PDEF,,•îpuals DEF.Í if tfie oeficil is positive ana zero otfierwise The standard deviations of PDEF,r are 35.9% for the sample used• n regressions ( i | and (2) of Panel A, 40.B% tor tue sample used m regression |3] of Panel A, 31.9% for régressons ( i |and (2) of Panel B, and 35 9% for regression (3| of Panel B ERP,_i is the implied market equity rsk premium at the enool year Í - 1.RIR,_i is the nominal interest rate minus inflation in year j DSP.F_) IS ttie default spread, defined as fhedifference in yields Detween Moody s Baa-rated and Aaa-rated corporate bonds at tfie end of year f — i TSPf_- is theterm spread, defined as the difference in yields (daily senes) between 10- and one-year constant maturity Treasuries atthe end of year r - 1 TAXR, is the statutoïy corporate tax rate during year t RGDP, is the real GDP growth tale dur,ngyear ! RSEO, _ i is the annual average of market-ad] usted returns during year f - i fiom one day before to one dayafter the file dale of seasoned equity offerings (SEOs) The average announcemeni effec! is calculated from 198Q. the firstyear the file date is available for most SEOs. All of the macroeconomic variables are presented m decimal form (i.e., a 5%ERP IS presented as 0.05) Both the dependent variable and the financing deficit are presented as percentages. In eacn•egression, we excluQe firm year obsen^ations where \AD,, > 400% cr \AE,i\ > 400% The l-slatistics are corrected•or correiatior both across aDse'vations of a gtven firm and across observations of a giver year (Roge's (1993|) and ft*nete-oskedasticity (White (1930))

(1)1969-2001

Coef i-Stat.

(2)1969-2001

Coef

Panel A. Financing DefKit (äeiineO with dividend payments inceasmg the deficil,

NDEF,iFDEF,.EBP._, xPDEF,,RIR;_, xPDEF,,DSP, ixPDEF.,TSP,_ixPDEF„rAXR.xPDEF,,RGDP, xPDEF,,RSEO,_ixPDEF.rConstantAd|. R^N

0.710.502.91

0 700.649

112.463

17 1824 22506

296

0.700.273.06

-0.56-2.03-3,70

0.503.09

0.510.657

112,483

f-Stat.

)

17.411.65399

- 0 8 6-0.42-2.52

1.132.67

246

(3)1981-2001

Coeff

0680332.951336.30

-3.67-0.53

5 12- 6 06

0 850 625

78,696

"anel B Financmp Deficî! (úefineó with diwdenú payments not alfectinq the value of the defici!)

NDEF,-PDEF,,ERP,_ixPDEF,,RlR;_ixPDEF„DSP, , >: P[5EF,rTSP;_, xPDEF,,TAXR. X PDEF,.HGDP, X PDEF,,RSEO,_|XPDEF„Constant

0 400.593.14

^ 0 140 676

1 12.467

10 3837 787 42

-0.69

0 390.453.27

-0.451-52

-3.420.192.90

-0.2t0 681

r 3.467

10304 79644

-1.030.57

- 3 . IS0.643.07

-1.17

0 370463.360 745.80

-3.54- 0 35

428- 3 32- 0 440664

76 682

r-stai

15.331.794.321 n0S3

-2.34-0.86

361-3.33

396

8815.M7 141.042 0-5

- 2 93- 1 0 3

4 5.-290- 2 5,?

relate the pecking order slope coefficient to the ERP estimated for each Iirm antilind qualitatively sitiiilar results. Our estimate of the HRP at the market level usint:only the well-esiahlished Dow M) companies wiih reliable accoufiling infortnatioiiis relatively conservative and is likely to tnideTstate the impori;tiice oí \ aluation inthe choice bctwccti debt and equity.

In regression (2) the estimated eoefticient ot) the interaction between theERP and the positive financing deficit changes little after controlling for the realrate of return on debt, the default spread, the term spread, the statutory tax rate,and the real GDP growth rate. The regression also shows that lirms fund a larger


proportion of their financing deficit with net debt when the corporate tax rate ishigher, consistent with the trade-off theory prediction that debt is used as a laxshield, although the relation is not statistically significant. The coefficient on theinteraction hetween the real rate of GDP growth and the positive financing deficitis positive and statistically significant, suggesfing that firms are more likely tofund their current growth opportunities with debt.

Regression (3) in Table 3 includes the average announcement effect of SEOsas an explanatory variable, using a shorter sample period because our RSEO se-ries does not begin until 1980. This variable measures the adverse selection costsof issuing equity, and has been used by, among others, Korajczyk, Lucas, andMcDonald (1990). Choe, Masulis, and Nanda (1993), Bayless and Chaplinsky(1996), and Korajczyk and Levy (2(K)3). The significantly negative sign of theinteraction between the average announcement effect and the positive financingdeficit is consistent with previous studies. That is, when this negative number iscloser to zero, firms issue more equity. Economically, a one-standard-dev i at i on(0.005) increase in the average announcement effect results in a decrease of 3>.0%of the financing deficit being funded with net debt. Relative to the impact of theERP. the average announcement effect (and therefore time-varying asymmetric in-formation) is of secondary importance in the choice of debt and equity financing.

If a firm pays out the cash flow it generated as a dividend, then the financingdeficit as defined in Panel A of Table 3 does not include that cash flow becauseboth assets and retained earnings are decreased by the dividend. However, if thefirm engages in a stock repurchase, then the financing deficit includes the cashflow because the deficit measures net external financing. In Panel B, we excludedividends and the change in cash in the definition of the financing deficit (i.e.,the payment of dividends does not affect the value of the financing deficit). Thecoefficient on the interaction between the ERP and the positive financing deficitbecomes even larger, suggesting a greater role of the ERP in the choice betweenexternal debt and external equity to fund the financing deficit.

The regression approach has both advantages and disadvantages. The ad-vantages include the summarization of information in the pecking order slopecoefficient, convenience for analyzing a large number of firms, and conveniencefor controlling for other factors in a multivariate framework. The disadvantagesinclude the potentially large influence of a few outliers and the oversimplificationof information. Furthermore, Chirinko and Singha (2000) question the validity ofShyam-Sunder and Myers' (1999) pecking order tests.

To gain additional insight, in Figure 4 we randomly select 100 firms eachyear and draw scatter-plots. We limit the number of randomly selected firms to100 per year because a larger number makes it difficult to visually identify mean-ingful patterns. If a firm funds 100% of its financing deficit with net debt, all ofthe points plotted will lie on the 45° line. A firm with negative net equity issuancewill lie on the left-hand side of the 45° line, while a firm with positive net equityissuance will lie on the right-hand side of the 45" line. We report the scatter-plotsfor only four years because those for other years with similar slope coefficientsare qualitatively the same. In 1975, when the slope coefficient is 0.91, only a smallnumber of firms deviate from the 45" line. In 1992, however, when the slope co-efficient is 0.42, several percent of the points are far to the right of the 45" line.


FIGURE 4

Scatter-Plots of Net Debt versus Net External Financing

The horizontal axis denotes net eslernal financing scaled by beginning-of-year assets, and the vertical axis denotes netdebt scaled by tieg inning-of-year assets. For each selected year. 100 randomly selecled observations are plotted. Thepeciiing order slope coefficient in Figure 3 is 0,909 for 1975. 0,768 for 1982, 0.482 for 1983. and 0.423 for 1992,

Graph B Year = 1983

-05

Graph A

1,5-

1

0.5

j r 1

tear

/

0,5

= 1975

45" line y

/

1

/

1.5 ;

1,5 -

1 -

0,5-

Ú

45° line /

• 0,5 1 1,5 ;

Net External Financing

Graph C. Year = 1983

Net External Rnancing

Graph D. Yeai - 1992

11.5-

1 -

0.5-

-O.5X'/^-0,5 -

«'line y

; 0,5 1 1.5 ;

*

Nat External Financing Net External Financing

These firms issue a lot of equity to finance their financing deficit or to retire deht.Only a few firms are noticeably to the left of the 45* line, suggesting that firmsonly infrequently repurchase shares in a quantitatively important manner.

B. Nested Logit Model for the Joint Decision

in the pecking order tests, we assume that the financing deficit is exogenous.However, a firm may decide jointly whether to issue securities and which secu-rity to issue. Therefore, we also estimate a nested logit model (Greene (2003),pp. 115-111). as do Gomes and Phillips (2007).'-' The nested logit model canalso potentially reduce the large influence of a few firms raising a large amount ofdebt or equity on the pecking order slope coefficient, because firms issuing 6% or

'^A nested logil model is similar to a multinomial logit model. However, u multinomial iogii modelassumes thai choices between any Iwo alternatives are independent of the other alternatives, while anested logit model only assumes that the choices are independent within a group or "nest" of alterna-tives.


60% of assets are both assigned the same value in the nested logit model. Anotherconcern regarding the pecking order tests is that the estimated coefficient fromthe financing deficit may simply reflect changing firm characteristics rather thanchanging market conditions (Flannery and Rangan (20()6)). We control for firmcharacteristics in the nested logit model.

Our nested logit model includes two decision levels. The first-level alter-natives are security issuance versus no security issuance, and the second-levelalternatives are equity versus deht issuance. Let Pr(i) equal either the probabilityof security issuance (/ — s) or the probability of tio security issuance (i — n), andPr(j|i) equal either the probability of equity issuance (j — e) or the probability ofdebt issuance (j = d) conditional on / = J. '* Then

(3)

and

(4) Pr(.) = ' ' 'P ( - ' ' "exp{ y¡a + r/j/J

where the inclusive values /,- = ln{exp(j:,e/3) -I- exp(jc,y/3)}, JCJ/. and v, refer to therow vectors of explanatory variables specific to categories (/,/') and (/), respec-tiveiy, and i]i refers to the inclusive parameters. We use nonissuers as the basealternative at the first decision level, and debt issuers as the base alternative at thesecond decision level. The nested logit model is estimated using full-informationmaximum likelihood.'^

We use the same set of explanatory variables, including both firm charac-teristics and market conditions, for all alternatives."' Firm characteristics includefinancial slack (the sum of cash and short-term investments), profitability, capitalexpenditures, Tobin's Q (market-to-book ratio of assets). R&D expenditures, thelogarithm of net sales, the logarithm of the number of years the firm has beenlisted on CRSP. the lagged leverage, the market-adjusted return during the previ-ous fiscal year, and the market-adjusted return during the following three fiscalyears. The results for the nested logit model aie reported in Table 4.'^ To as-sist in gauging economic significance, we vary each explanatory variable by plusor minus one standard deviation from its sample value (a two-standard-deviationchange), and then we average the change in the predicted probability over allfirms in the sample in order to obtain the economic effects, holding other variables

'" A firm is defined as issuing debt if the net change in debt is at least 5% of its beginning-of-year assets. Similarly, a firm is defined as issuing equity if the nei change in equity is at least 5% ofits beginning-of-yc;ir asscis. For convenience, lirni years when both debt ;md equiiy are issued arcexcluded in the nested logit regressions. For characteristics of linns issuing twHh debt and equity, seeHovakimian cl al. (21)04). We keep ihese lirms in other analyses,

'^Several previous studies examine ihe choice between debt versus equity ñnancing in isolationusing a logil model (e.g.. Jung et al. (19961) or a probit mode! (e.g.. Mackie-Mason ( 1990)), implicitlyassuming that the choice between issuing versus not issuing security is exogenous.

"•If we restrict both ;;., = I and r;,, = I. then we have a multinomial logit model.'^We are not aware of any statistical packages that are able Eo adjust nested logit irgressions for

clustering.


TABLE 4

Nested Logit Model of Securities Issuance Decisions

We esiimate a nested logit model of the following siructure:

No

—

SecuriLyIssuance

DebtISEuencs

\

EquityIssuance

We use nonlssuers as the base alternative at the first decision leuei. and debt issuers as the base alternative at the seconddecision level. Firms that issue botli debt and equity in the same yeaf are excluded (rom the sample, which covers 1969-3301. ^ 0 is the change in debt and preferred stock (Compustal items 181 -i- 10 - 35 - 79). ¿IE is the change in equityand ccnvertibie debt (items 6 - 181 - 10 + 35 + 79) minus Ihe ctiange in retained earnings (36) A firm is defined asissuing debt if AD/A,^ i > Q.05. Similarly, a tirm is defined as issuing equity if AE/Ai_, > 0.05. CASH is the sumof cash and short-term Investments (1) scaled by assets. OiBD is operating Income before depreciation (13) scaled byassets CAPEX is the capital expenditure (128) scaled by assets. Q is the sum of Ihe market value of equity and the bookvalue of debt divided by the book value of assels. R&D is the research and development expense (46) scaied by assetsand IS set to zero if it is missing. RSDD is a dummy variable that equals one if RSD is missing and equals zero otherwise.SAL£ is the log of net sales (12) AGE is Ihe naturai log of Ihe number of years the tirm has been listed on CRSP BL isbook leverage, defined as bcxik debt (items 181 + 1 0 - 3 5 - 79) scaled by assets MAR^^i is measured as Ihe differencebetween the tirm raw return and Ihe valu e-weigh ted market return in the preceding fiscal year MAR[.ti,|.,3 is measured asthe difference between the firm raw return and the value-weighted market retum in the foliowing three fiscal years. If a firmIS delisted. ils post-event three-year raw return is calculated by compounding the CRSP va i ue-weighted market return forthe remaining months. ERP, _ i is the impiied mari<et equity risk premium at ihs end of year ( - 1 R[R,_ i is the nominalinterest raie minus inflation in year t. DSP, _ , is the default spread, defined as ihe difference in yields between Moody'sBaa-rated and Aaa-rated corporate bonds at the end cf year f - 1. TSP, _ ] is the term spread, defined as the difference inyieids (daiiy series) between 10-and one-year constant maturity Treasuries at Ihe end cf year 1 - 1 . TAXR; is the statutorycorporate lax rate during year t. RGDP| is Ihe real GDP growth rate during year f. To help gauge the economic effecls.we vary each explanatory variable from one standard deviation below to one standard deviation above its sample vaiue.and use the coefficients trom the nested logil regression to calculate the change in the predicted probability, holding allother variables fixed. We then average the change in the predicted probability over ali firms m the sampie to gel economiceffecls. The (-statistics are calculated using heieroskedastic consistent standard errors (While (1980)).

First-Level Decisicn: Second-Levei Decision:Issuing (vs. Not Issuing) Equity (vs. Debl)

CASHir-101BDj,_iCAPEXy(_ J0,,-,R&DD,,_,RSDii-1SALE;r_,AGE,,BL,, _ 1MAR;,_,MAR,r4.i u3ERP,_,RIR, 1DSP,..,TSP,_,TAXR,RGDP,N

Coefl.

-1,051-0.793

3.2130.3410.0711.5650-002

-0.2280.1770.477

-0.068-3.164-3.488

-13.417-8.514

1,271•1.452

82,653

I-Stat,

-15.59-7.1527.1716.173.866.2'10-36

-20.323.17

22.12-11.67-7.92-9 .36-5.55

-11.148.44971

EconomicEffect

- 7 . 1 %-4-5%11.3%15.9%

1.6%4.7%0.1%

-8 .4%1.6%

14.8%- 5 . 1 %-5.4%-4 .6%-3,0%-4.4%

3 7%4 2%

Coeff.

0 369-1.218

0.9190.3840.2363.452

-0.134-0.107

1.0350.384

- 0 106-7.462

3.51017.0053.8890.B35

-4.324

f-Stat.

3.8B-10.50

7.0128.629.35

14.07-17-20-6.3315.3921.08

-11-93-13.30

6364.863.312.83

-6 .04

EccrramicEffect

2-1%-5 .6%

2.7%14-7%4.3%8.3%

-9 .3%-3 ,2%

7.6%9.9%

-6 .5%-10.3%

3.8%3.2%1.7%2.0%

-3 .4%

fixed. Because our results are generally consistent with other results in the litera-ture, we will only highlight a few of the results.

We first hriefiy discuss results for the first-level decision: security issuanceversus no security issuance. Consistent with the pecking order theory, firms thathave more cash and higher profitahility are less likely to access external capi-tal markets, while growth firms, as measured by capital expenditure, Tobín's Q,


R&D, and the preissue one-year market-adjusted firm return, are more likely toaccess external markets. Older firms rely less on external financing. Macroeco-nomic variables also appear to be important determinants of whether to accessexternal markets.

We proceed to discuss results for the second-level decision: equity issuanceversus debt issuance, conditional on the decision of security issuance. Our resultsare generally consistent with the existing literature. Firms with more cash aremore likely to issue equity. Profitable firms are more likely to issue debt. Firmswith more growth opportunities, as measured by capital expenditure. Tobin's Q.R&D. and preissue one-year market-adjusted return, are more likely to issue eq-uity. Larger and older firms are more likely to issue debt.

Confirming the importance of market timing. Tobin's Q and the past market-adjusted firm return are among the most important explanatory variables in thedecision to issue equity, both statistically and economically. Holding other vari-ables at their sample values, if Tobin's Q is increased from one standard deviationbelow to one standard deviation above its sample value, the prof>ensity to issueequity increases by 14.7%. Similarly, if the past market-adjusted firm return isincreased from one standard deviation below to one standard deviation above itssample value, the propensity to issue equity increases by 9.9%. Firms that subse-quently underperform are also more likely to issue equity, and this variable has alarger economic significance than most other variables. An increase in the futuremarket-adjusted return from one standard deviation below to one standard devi-ation above results in almost a 6.5% reduction in the propensity to issue equity.This provides further support for the market timing theory.'**

Consistent with the static trade-off theory, high leverage firms are more likelyto issue equity rather than debt during 1964-2001. If we increase the lagged bookleverage from one standard deviation below to one standard deviation above itssample value, the propensity to issue equity increases by 7.6%.

We are interested in whether the implied ERP has additional explanatorypower after controlling for firm characteristics. If the lagged value of the ERFincreases from one standard deviation below to one standard deviation above itssample value, the average propensity to issue equity instead of debt decreasesby 10.3%. Economically, it is more significant than all other variables except tbelagged firm level Tobin's Q.

When the RIR is higher, firms are more likely to issue equity. Economically,an increase from one standard deviation below to one standard deviation above

"'jungelal. (1996) include the post-issue firm return as a proxy for cxpecied mis valuation in a logitmodel for finn.s' choice between debt and equity issuance, although they do not find this variable to bestaiisticully significant tora small sample of U.S. firms from 1977 to 19S4. Consislenl with our resiills,DeAngelo el al. (2009) also find a statistically significant negative relation beiween the probability ofconducting an SEO and future three-year market-adjusted returns for U.S. firms from 1982 to 2001.However, they find that the propensity to issue equity increases by only \.^% for a swing of a 75'iiloss to a 75% gain over three subsequent years, far below our 6.3%. The difference in results appearsto be primarily due to two reasons: i) The definitions of equity issuers are difieren!. They use SEOs,whereas we use the change in the bix>k value of equity (net of increases in retained earnings), whichincludes private placements and stock-financed acquisitions, ii) Their \.5% is the percent of equityissuers among all firms, while our 6.5% is the percent of equity issuers aniong debt issuers and equity


its sample value is associated with an increase of 3.8% in the propensity to issueequity. The defauit and term spreads have an even more modest effect on the debtversus equity choice. Inconsistent with the static trade-off theory that views thelax rate as a major factor in the decision to issue debt, the tax rate has only asecondary effect on the propensity to issue debt or equity.

The statistical and economic importance of our cost of capital proxies isconsistent with the hypothesis that firms time their securities offerings to takeadvantage of intertemporal variation in the relative cost of different sources ofcapital. One could also interpret these results as being consistent with the staticirade-off model, with firms moving to a new optimum as the relative costs of debtund equity change. Traditionally, researchers have assumed that the relative costsdo not vary over time. Instead, researchers have assumed that firm characteristicsmight change over time, but the market-determined costs of debt and equity donot change.

In summary, the nested logit results in Table 4 suggest that Tobin's Q. thepreissue stock price run-up, and the implied ERP are the three most important de-terminants of firms' choice between equity and debt.'^ This is consistent with themarket timing theory, although not necessarily inconsistent with the static trade-off theory with an optimal target that depends on the time-varying relative costsof debt and equity and growth opportunities. To further distinguish the alternativetheories, in the next section we investigate how historical market conditions influ-ence a firm's current leverage through their important role in the firm's historicalfinancing activities.

IV. Effects of Market Timing on Capital Structure

Firms may adjust their capital structure with internal funds or external funds.The pecking order theory posits that external funds are more expensive than in-ternal funds and external equity is more expensive than external debt. Therefore,securities issues, especially equity issues, should be rare and only have a materialimpact on the capital structure of firms with insufficient internal funds. The mar-ket timing theory is similar to the pecking order theory in that observed capitalstructure is the outcome of historical external financing decisions, rather than aprimary goal in itself.

In contrast, in the static trade-oft" theory, firms issue securities to adjust to-ward their target leverage. Once target leverage and partial adjustment are prop-erly controlled for, past securities issues and market conditions should have noimportant impact on current leverage (although with adjustment costs. Fischer,Heinkel, and Zechner (1989). Hennessy and Whited (2005), Ju, Parrino,Poteshman, and Weisbach (2005), Leary and Roberts (2005), Strebulaev (2007).

'''We did several robusttiess checks: i) using a multinomial logit model even if our unrcported testshows ihai choices between any iwo altematives are not independent of the other alternatives; ii) usingIhe value-weighted market-to-b(xik ralio of equity of all N YSE-listed timis prior to fiscal year / as analternative proxy for the cost ofequily at the market level; iii) including convertible preferred stock inequity; and iv) excluding firm-year observations with major mergers and acquisitions and spin-offs.Our results are not qualitatively affected.


and others allow for a roie). Therefore, it is important to examine the effects ofpast securities issues and market conditions on observed capital structures in or-der to compare the relative strength of each theory. This is especially importantbecause there is widespread agreement that market timing considerations appearto be important in determining securities issues (see Alti (2006) and Hovakimian(2004). (2006), among others). The main debate is regarding the persistence ofthe effects of securities issues and market conditions on capital structure.

To control for target leverage when estimating the effects of past securitiesissues on current leverage, we estimate the following regression:

(5) L;; - /(TARGETXEVERAGE_PROXIES,v_

,_t_, xPDEF,,_t),

where L-,, is the leverage ratio of firm / at the end of year t, k is the lag length inycitrs. PDEFy,_i equals DEF,V_Í if DEF,,_A > 0 and zero otherwise (DEF,V_A isthe change in assets minus the change in retained earnings scaled by beginning-of-year assets for firm Í in year i - ^ ) , and ERPf_i_i is the implied ERP at the end ofyear t - k- 1. Target leverage proxies include lagged firm characteristics, laggedor current macroeconomic variables, and year dummies. We examine whether theERPÄ+I years ago and firm /'s financing deficit Ä: years ago still have an impact onthe firm's current leverage. The static trade-off theory predicts that the coefficientson ERP,^t_i X PDEF,,_i and PDEF/i-t should be insignificant when k is large.The market timing theory predicts that the effect of ERP,..i._ ] x PDEF,,_;(. on year ileverage should be positive and statistically significant until k becomes very large.

Table 5 reports pooled OLS results with book leverage (Panel A) or marketleverage (Pane! B) as the dependent variable for k — 0, 4, 6. and 8. To removethe effects of clustering on the estimated standard errors, we report /-statisticscorrected for correlation both across observations of a given firm and across ob-servations of a given year (Petersen (2(X)9)). Since the results regarding the targetleverage proxies are generally consistent with previous studies, we focus our dis-cussions on the effects of the historical ERPs and financing deficits. Also, wefocus our discussions on book leverage, since there is evidence that firms onlyslowly undo the effect on market leverage induced by stock price movements(Welch (2004)). In the market leverage regressions, the large /-statistics on Q arepartly due to the mechanical relation induced by the market value of equity beingin tbe numerator of Q and the denominator of the dependent variable.

The regression ( I ) results with /: — 0 are generally consistent with the resultsin Table 3. The coefficient on the interaction between the ERP and the financingdeficit is statistically significant. The effect of the financing deficit on book lever-age is (3.687 X ERP,_| + 0.242) x PDEF,,. Con.sistent with the market timingtheory, the effect of the financing deficit on leverage is positively related to theimplied ERP. The minimum estimated ERP is -0.043 (—4.3% per year) in 1999,and the maximum is 0.114 (11.4% per year) in 1974. For a firm with a financ-ing deficit of 10% (the sample mean) in 1999. the effect on its book leverage is(3.687 X ( -0.043) +0.242) x 10% = 0.83%. For a firm with a financing deficit of10% in 1974. the effect on its book leverage is (3.687 x 0.114 + 0.242) x 10% =6.62%. Thus, die financing deficit results in a smaller increase in book leverage


TABLE 5

Effects of Historical Financing Activities and Market Conditions on Leverage

The tollowing equation is estimated using firms Irom the period 1969-2001 :

L,, = r(TARGET-LEVERAG£J'ROXiES;r_,,ERP,_),_, x PDEF,,_k,

Tiie dependeni variable. Lu. is either book leverage or markel leverage of firm i st the end of year t. Book leverage isdefined as book debt (items 1B1 + 10 - 35 - 79} divided by book assels (item 6) Market leverage is defined as book öetjtdivided by market assels (items 181 + 10 - 35 + 25 x 199) Target proxies include firm characteristics, market conditions,and year dummies. 0 is Ihe sum of Ihe market value of equity and the book value of debt divided by the book value ofassets. R&D is the research and developmeni expense (46) and is set to zero if it is missing. R&DD is a dummy variablettiat equals one if R&D is missing and equals zero otherwise, CAPEX is the capital expendittjre (128) SALE is the log ofnel sales (12). OIBD is the operating income before depreciation (13). TANG is ihe net property, planl, and equipment (B),R&D, CAPEX, OIBD, and TANG are scaled by end-of-year assels. ERP(_(,_ i is the implied markel equity risk premium ati t ieendofyear f - k - 1 RIR,_| is the nominal interest rate at the end of year [ - 1 minus inflation in year i. DSP(_i is thedefault spread at the end of year r - 1 TSPr_, is tfielerm spread althe end of year f - I.TAXRt is ihe statutory corporatelax raie during year ( RGDP; is the real GDP growtn rate during year t. PDEF,,_,, is the positive financing deficit duringfiscal year í - f<, scaled by total assets at Ihe end of year t. PDEF,,_j, equals zero if Ihe financing deficit during fiscalyear 1 - h is negative. Firm year observations where PDEF, ,_K > 10 are dropped The standard deviations of PDEF,,,PDEF,f,.a, PDEF,,_6, andPDEF,,_B are, respectively, 16.1%, 16.0%, 16 7%, and 16,2%. Year dummies and theinterceplare included, bul thetr coefficients are no! reported. We repori l-stalislics using standard errors corrected for correlationacrossboihobservaiionsof a given firm and observations of a given year (Rogers (1993)),

Panel A. Book Leverage

Q r ( - 1R&DD,,_,R&D,,_iCAPEX,, _ ,SALE,,_iOIBD,f_,TANGj,_,ERPt-1RIR,_iDSP,_,TSP,_,TAXR,RGDP,ERP,_k_iX PDEF,,_kPDEF,,_,Year dummiesNR^

Panel B. Market Leverage

R&DD i _ 1R&Dit„iCAPEX;, _ ,SALE,,_|OIBD,r_,TANG,,_iÍRP,-,RIR,_iDSP,_iTSP,_,TAXR,RGDP,i£RP,_(,_l X PDEF([_,,PDEF,,. ,Year dummiesN

k

Coeff,

-0.0370 028

-0,4560.0550.031

-0,3470.002

-0,4790,189

-0,1980.037

-0.525-0.159

3.6870,242

Yes111,413

0,217

-0.0880 026

-0,624-0,066. 0 021-0.451

0,028-0,415

0-229-2,373-0.265-0.428-0,523

1,3880.136

Yes151,413

0.399

(1)= 0

f-Slat.

-23,54709

-7.931.86

16 86-9.34

0,13-1,78

1,17-0,18

0,10-3.66-0,80

9,0114,46

-26,505.74

-10,38-2.3421,51

-8.821.82

-1,410,89

- 1 75- 0 63-2.01-2,57

3,789,77

k

Coeff.

-0,0300-020

-0,4800,1260,032

-0,439-0,020-0,284

0,256-0.514- 0 104-0.474-0.106

2,1700,044

Yes68,7570,182

-0,0990.018

-0.669-0,044

0,021-0.574

0,016-0,471

0,369-2.077-0.129-0,340-0,523

1,9050.015

Yes68,7570.393

(2)= 4

t-Slat,

-11.454.53

-8.452.38

15,91-9.60- 1 44-1,10

1,43-0,43-0,27-2,56-0,48

4.432,53

-19,123,60

-11.93-0.9517.33

-9.271.07

-1.932,07

-1,55-0,43-1,50-3.27

3,960,79

k

Coeff.

-0,0260,020

-0.4860.1080,033

-0.488-0,023-0.476

0.317-0,528-0,096-0.506- 0 129

1,9090,017

Yes55,2360,181

-0-1010.017

-0.684-0,043

0.021-0,634

0,018-0.594

0,428-2.044-0,169-0,351-0,569

2,146-0.014

Yes55,2360.386

(3)= 6

I-Sial,

-8,36A.29

- 7 642.14

15.87-9.86-1.68-1.48

1,88-0,45-0,26-2,75-0,50

4,191.23

-19,193.20

-11.31-0,9516.22

-10,081.23

-1.702,12

-1.35-0,52-1,49-2,19

4,49-0.91

k

Coeff.

-0.0230,019

-0,4980,0830,033

-0.524-0.026-0.332

0,390-0,325-0.090-0.606-0.071

0,8670.028

Yes44,6300,179

-0.0990.016

-0,676-0,041

0.022-0.669

0018-0.498

0,553-1.397-0,188- 0 480-0.436

0.7540-016

Yes44,630

0.384

(4)- 8

r-Stat.

-6,583,85

-7.411,57

15 79-9.51-1,76-1,00

2,26-0.31-0.20-3.18- 0 27

1,151,00

- 1 8 752,99

-10.72-0,8314.78

-10,541.13

-1,312,80

-1.10-0.57- 2 1 1-2,07

1040 61


when the cost of equity is low (1999) than when the cost of equity is high (1974).a pattern not predicted by the pecking order hypothesis. The total effect of theñnancing deficit on market leverage in Panel B also depends on the magnitude ofthe ERP. although the quantitative effect is smaller.

In regression (2) with k ^ 4, the effect of the financing deficit five years agoon current hook leverage is (2.170 x ERP,_5-f 0.044) x PDEFif_4. For example,a \0% financing deficit in 1996, when the implied ERP was low, would increase alinn's book leverage five years later by only (2.170 x (-0.004)+0.044) x 10% =0.35%. In contrast, a 10% deficit in 1974, when the implied HRP was high, wouldincrease book leverage five years later by (2.170 x O.I 14 + 0.044) x 10% =2.91%. The difference in the impact on book leverage of the 10% financing deficitbetween 1974 and 1996 is 2.56%.

The difference in the impact is economically significant. In our sample, thestandard deviation of the change in book leverage during one year is only 10.08%.consistent with the high persistence in leverage documented by, among others.Kayhan and Titman (2007) and Lemmon et al. (2008)). Relative to the standarddeviation, a 2,56% difference in leverage is not a small number. It should be notedthat the role of the cost of equity capital is understated in this paper because ourmeasure at the market level does not capture the cross-sectional variations at thefirm level.

The eoefficient on the interaction term continues to be statistically significantin regression (3) with k = 6, suggesting that the ERP six years ago still has animpact on current leverage. The coefficient on the interaction term becomes muchsmaller in regression (4) with k = ^, however, reassuringly suggesting that theERP's effect on future leverage does not implausibly persist forever.

Hovakimian (2006) and Kayhan and Titman (2007) suggest that the impor-tance of the external finance weighted average of historical market-to-hook ratiosin Baker and Wurgler (2002) is driven by the mean value of historical market-to-book ratios. They argue that the historical mean market-to-book ratio captures thecross-sectional variation in growth opportunities, which is one of the major deter-minants of long-term target leverage. Our measure of the cost of equity capital althe market level largely captures time-series variations instead of cross-sectionalvariations. The long-lasting effect of historical ERPs through their influence on fi-nancing decisions is inconsistent with the static trade-off theory, although it is notnecessarily inconsistent with a dynamic trade-off theory with costly adjustment.

Our results also complement those of Alti (2006), who restricts his analysisto firms that have issued equity. It is possible that at least some debt issuers issueddebt instead of equity because of a high ERP. Therefore, although using onlyequity issuers lo examine the impact of market conditions on capital structure isinformative, it provides an incomplete picture.

V. Estimating the Speed of Adjustment

In the previous section, we regress leverage on a set of variables that predictleverage in order to generate a target leverage equation. In the Table 5 analysis,we do not control for firm fixed effects. It is possible that past securities issuescapture unobserved firm characteristics that determine current target leverage. If


this is true, then the persistent effects of past securities issues are consistent withthe trade-off theory. Among recent studies, Flannery and Rangan (2006) estimatea dynamic panel model with firm fixed effects to address this issue.

The dynamic panel model with firm fixed effects can be summarized in tbefollowing two structural equations, assuming that target leverage is determined byobserved firm characteristics and unobserved characteristics that are captured byfirm fixed effects:

(6) Li, - Li,-1 ^ 7(TL(f - Li,- \ ) + £,>

and

where L,, is the leverage ratio of firm / at the end of year i, TL,, is target leverage,Q-, is the firm fixed effect, and X¡,_\ is a vector of lagged firm characteristics offirm Í, current or lagged macroeconomic variables, and year dummies. If TL/, isobservable, then we can estimate equation (6) to find the SOA toward the targetcapital structure, 7. Unfortunately, we cannot observe target leverage. Therefore,we have to rely on a reduced form specification:

(8) Li, - (1 - 7 ) ^ / - i +7Qi + 7/3X,-,_| +e,,.

Two properties are well established for a dynamic panel in which the laggeddependent variable is an explanatory variable (Hsiao (2003)). First, the estimatedcoefficient on the lagged dependent variable with a pooled OLS estimator ignor-ing firm fixed effects is biased upward under reasonable assumptions. Second, theestimated coefficient using the standard approach of mean differencing the modelis biased downward, especially when the time dimension is short (Nickell ( 1981 )).In essence, the mean differencing estimator first takes the mean for each firm:

(9) Li

It then subtracts equation (9) from equation (8) to get rid of firm fixed effects:

(10) Lu~Li - {I

Since tbe average firm has continuous Compustat data for only about sixyears, the coefficient on L,,_ |, 1 - 7, may be biased substantially downward.Recognizing this problem, Flannery and Rangan (2006) focus on market leverageratios and use lagged book leverage as an instrument for their lagged dependentvariable, lagged market leverage. They report an SOA toward target market lever-age of 35.5% per year (regression (7) in Table 5). It is not clear, however, thatlagged book leverage is a valid instrument for lagged market leverage, becauseat least some shocks are likely to affect both book leverage and market lever-age. Similarly, they report an SOA toward target book leverage of 34.2% per year(regression (2) of Table 5),

With a large dynamic panel data set, we are able to evaluate the sensitivityof the estimated adjustment speed with respect to the time dimension with some


experiments. We first focus only on firms with data for exactly five consecutiveyears in Panel A of Table 6. For book leverage, the adjustment speed is 15.6% peryear ( I - 0.844, v/here 0.844 is the coefficient on lagged book leverage) when thepooled OLS estimator ignoring firm fixed effects is used; the adjustment speed is73.8% per year when the mean differencing estimator is used. For market lever-age, the adjustment speed is 13.6% using the pooled OLS estimator ignoring firmfixed effects and 76.5% using the mean differencing estimator. The gap betweenthe OLS estimates and the mean differencing estimates, which are biased in op-posite directions, is huge.

TABLE 6

Time Dimension and the Speed of Adjustment toward Target Leverage

We eslímate ihe following eguaiions:

The first equation is estimated using the pooled OLS estimator. The second equation is estimated using the mean differ-encing OLS estimator. The dependent variable is either book leverage or market leverage of firm i al the end of year I Bookleverage (BL) is defined as book debt {items 181+10 — 35 — 79) divided by book assets (item 6) Market leverage {ML) isdefined as book debt divided by market assets {items 181 -• 10 - 35 + 25 x 199). X includes lagged firm characteristics,market conditions, and year dummies, Û is Ihe sum of the market value of equity and the book value of debt divided bythe book value of assets. R&D is the research and development expense (46) and is set to zero if it is missing, R&DD is adummy variable that equals one if R&D is missing and equals zero otherwise, CAPEX IS the capital expenditure {128) SALEis the log of net sales (12). OIBD is the operating fncome before depreciation (13), TANG is the net property, planl, andequipment (8) R&D, CAPEX, OIBD, and TANG are scaled by assets, ERP,_ i is the implied market equity risk premiumat the end of year t - 1 RIR,_i is the nominal interest rate at the end ol year t - 1 minus inflation in year r, DSP, _ , isthe default spread at the end of year I - 1. T3Pi_i is the term spread at the end of year ( - 1. TAXRi is the statutorycorporate tax rate during year f. RGDP, is the real QDP growth rate during year f Panel A presents results for firms listed onCompustat for e:(actly five consecutive years This restriction results in a sample of 894 firms for whicfi there are [our yearsof lagged data. Panel B presents results for 425 tirms continuously listed on Compustat for the 30 years from 1972 to 2tX)1for which there are 29 years of lagged data. Panel C examines the same 425 firms as m Panel B, but uses only five years oldata during 1997-2001, In Panel C, we drop DSP, TSP, TAXR, and RGDP to avoid perfect multicollinearity. For brevity, thecoefficients on year dummies and the intercept are not reported For the mean differencing regressions, the "within' R^statistics {i,e., R statistics from running OLS on the mean differenced data) are reported The pooled OLS t-5tatistics useheleroskedastic consistent standard errors (White (1980), further adjusted for correlation across observations ol a givenfirm (Rogers ¡1993))

Book Leverage Market Leverage_

Without RrmFixed Effects

Coefl, I-Stat.

With FirmFined Effects

Coeff. f-Slat,

Without FirmFined Effects

Coeff i-Stat

Panel A. Regressions on Firms Continuously Usted on Compuslal lar Exaclly Five Years

BL,-|_,ML„_tQ,r^iRaDD,, _ 1R&D,,_,CAPEXi,_iSALE,,_,OIBD,,_iTANG„„ ,ERPr^iRIR,_,DSP,_-,TSP,_,TAXR,RGDP,Vear dummiesR 2

N

0,844

-0.010-0,002-0,089

0.0560,006

-0,1070,002

-0,313-C.150-0,852

1.1270.309

-0.617Yes

0,7183.576

65.6

- 5 1-0 ,5-2 ,4

1,84,3

-5 ,70,2

-1.1-0 ,6-0 ,6

1,70.8

-2 ,3

0,262

-0,011-0,031-0,119

0,0580,010

- 0 0 9 60 023

-0.326- 0 1 8 1-0,314

1,2990.687

-0,760Yes

0,1643,576

12,3

-4 .3- Z 2-2 ,2

1,52.1

-3 ,80,7

-0 ,9-0 ,7-0 ,2

2,01,5

- 2 4

0,864-0.002

• 0,006-0.179

0.1170006

-0,072-0.012-0,609-0,039-1,643

0,597-0.525-0,999

Yes0.7413,576

66.4-1 .2

1,2-6 ,0

3.54.0

-3 ,6- 1 0- 1 8-0 .1-0 ,9

0,8- 1 4-3 ,0

With FirmFixed Effects

Coeff.

0.235-0,002-0,018-0,182

0,1610,031

-0,088- 0 020-0.468-0.110-0,643

0.9410,212

-1,148Yes

0,2223,576

r-Stat

10,0-0 .6- 1 2-3 ,1

3.85,9

-3 ,2-0,5-1 ,2-0,4-0 .4

1,30,4

-3 .4

(contirHjed on next page)


TABLE 6 (continued)

Time Dimension and the Speed of Adjustment toward Target Leverage

BiMk Leverage

Without FirmFixed Ettects

Coeff, t-Stal,

With FtfmRxed Effects

Coetf. t-Stat

Markel Leverage

Wilhoul FirmFined Effects

Coeff,

i'anel S, Regressions on Firms Continuously Listed on Compustat during 1972-2001

ML,,_,

o,,_,R&DO,,_ 1R&Di,_,CAPEX,f_,SALE,,_iO1BD,,_,rANG,,_iERP,_,

ÛSP,_,rap,_irAXRtRGDP,••ear dummies

f j

0.907

-0,0010,001

-0,0200.0770.DG4

-0,083-0.013-0.021

0.036-0,940-0,220-0-028

0,013Yes

0,86012,325

171,2

-0 .90.5

-0 .74,58.9

-7 .1-2 ,7- 0 . 3

0.6- 2 2- 1 . 8-0-3

0,2

0,803

-0.002-0,001

0.0770,086

-0-002-0.099-0,012-0.048

0.057-0-906-0.212-0,071-0,007

Yes0.674

12,325

143,6

- 1 , 8- 0 . 3

1,75.5

- 2 . 0-9 ,1- 1 . 4- 0 , 6

0,8- 2 , 2- 1 4-0 ,7-0 ,1

0.890-0.004

0.001-0-149

0.1730.002

-0,093-0-022-0,354

0.252-4.227-0,014-0,256-0,350

Yes0.849

12.325

r-Slat,

153 3- 3 , ' !

0,5-5 -9

8.05-0

- 7 . 1- 4 , 0-3 .4

3,1-7 ,0-0 ,1-2 ,1-4 ,4

With FirmFixed Effects

Coetf,

0,754-0.006

0-000-0,103

0.1690,007

-0,125-0.007-0,401

0,309-3,679

0,012-0.293-0.390

Yes0,658

12.325

t-Stat,

109.8-3 .9

0.2-1 ,8

8,54.3

-9 ,1-0 ,7-3 .8

3 6-7 ,1

0.1-2 .3-4 .8

Panel C. Regressions Using Only Five Years oí Data ( 1997-200 J) on firms Continuously Listed or) Compustat during1972-2001

ML,,_,J,t-1

K&D,,_iCAPEX;, _ ,3ALE,,_iOIBD,,_,TANQ,,_,ERP,_iHIR,_,Year dummies

N

0 926

0,001-0.002-0.131

0.1220.002

-0,054-0.009

0,2290.195

Yes0,8371,700

75,7

0,3-0 .5-1 .8

2.31,6

-1 .3- 0 . 8

0,60,8

0,300

- 0 0040.0150.3490,179

-0,019-0,134

0,15202290.100

Yes0.1551.700

6.2

-0 ,80,71,32,4

- 1 . 4-2 .2

2,70,604

0,9210,002

-0.001-0,330

0,181-0.002-0.066-0.016-1,799

1.335Yes

0,7871.700

59.61.0

- 0 . 2- 3 . 9

3,1- 1 , 8- 2 . 1- 1 . 2- 3 , 3

3.7

0.1590,0040.0130,5120,4000.032

-0,2150,027

-1,3701,552

Yes0,1921,700

3,70.60,41,53.81,9

-3 ,70,4

- 2 , 6^,3

In Panel B of Table 6. we keep only the 425 firms continuously listed onCompustat for 30 years from 1972 to 2001. While the OLS estimator ignoringfirm fixed effects suggests a slightly slower adjustment toward target book lever-age for this longer panel of firms than for tbe short panel (9.3% per year for firmswith 30 years of data vs. 15.6% per year for firms witb five years of data in PanelA), when tbe mean differencing estimator is implemented, a mucb slower SOAis estimated for firms witb 30 years of data than for firms with five years of data( 19.7% per year in Panel B vs. 73.8% per year in Panel A). Even though theimplied SOA using the mean differencing estimator is biased upwards in PanelB, it still provides an adjustment speed of only 19.7% per year for book lever-age and 24.6% for market leverage. Tbe gap between tbe OLS estimates ignoringtirm fixed effects and tbe mean differencing estimates is greatly reduced for tbislonger panel of firms. If the true adjustment speed lies between the OLS esti-mates ignoring firm fixed effects and tbe mean differencing estimates, tbe resultshere suggest a mucb slower adjustment speed tban is suggested in Flannery andRangan (2006).


II should be noted that not all the differences between Panels A and B arenecessarily due to the differential time dimension bias. Panel A is intensive inrecent IPOs, whereas Panel B is not. To address this issue, in Panel C we furtherexamine the 425 firms that are continuously listed on Compustat from 1972 U)2001, In the regressions, we restrict the use of data to a five-year period from 1997to 2001 for these relatively old firms. The estimated coefficients on the laggeddependent variable using the mean differencing estimator are close to those inPanel A and substantially different from those in Panel B, suggesting that themain reason for the different results between Panels A and B is the differencein the time dimension, rather than the longevity of the firms. We also restrictthe use of data to other five-year periods (1972-1976, 1977-1981, 1982-1986,1987-1991. and 1992-1996) for the same 425 firms. These unreported results areessentially the same as what we obtain for the period 1997-2001.

To avoid the short time dimension bias, early studies focus on first-differencedinstrumental estimators and GMM estimators (Anderson and Hsiao (1981).Arellano and Bond (1991), among others). These estimators rely on first differ-encing or related transformations to eliminate an unobserved firm-specific effect,and use lagged values of endogenous or predetermined variables as instrumentsfor first differences. However, these estimators are found to incur substantial finitesample biases when the autoregressive parameter is close to one, largely becausefirst differences of highly persistent data series are close to being innovations.These estimators are thus not reliable for our data because firm leverage is highlypersistent. Arellano and Bover (1995) propose a system GMM estimator (alsocalled extended GMM), which imposes additional moment restrictions. Blundelland Bond (1998) suggest that the system GMM estimator performs better withpersistent data series than first differencing estimators. This is the procedure usedby Antoniou et al. (2008) and Lemmon et al. (2008).

Specifically, the system GMM estimator takes the first difference of equation(8):

(U) U-Lit-x = {\--f){Li,-r-L,-2)+'rß{Xi,-i -X,v_2)+ £;; - eV,.

Equations (8) and ( 11) are then simultaneously estimated as a "system." The sys-tem GMM estimator uses the lagged differences (¿«_2 — ¿if-3, - •. ^/i - ^ÍÜ) ^instruments for equation (8) and the lagged levels (¿,7-2, • • •, ¿.¡o) as instrumentsfor equation (11). The set of moment conditions for the system GMM estimatortends to explode as the time dimension increases, however, resulting in finite sam-ple problems.-" Proper choices of a smaller set of moment restrictions could help(e.g., Antoniou et al. (2008)). although the literature has not yet provided clear-cut guidelines for such choices when implementing the system GMM estimator,Roodman (2009) cautions that the system GMM estimate of the coefficient on thelagged dependent variable could be very sensitive to the choice of instruments.

Hahn et al. (2007) show that the usual first-order asymptotic advice of usingthe full set of moment conditions does not provide proper guidance in the dynamic

-'*A finite sample may have insufficient information to estimate a large instrument matrix. Also,a large set of instruments could overfit the endogenous variables.


panel data model when the autoregressive parameter is close to one. They alsoshow that a long differencing estimator, which alleviates the problem of weakinstruments and relies on a smaller than the fnll set of moment conditions, ismuch less biased than the GMM estimators. In a simulation, they show that ifihe true autoregressive parameter is 0.9, the system GMM estimate is only 0.664,whereas the long differencing estimator produces an estimate of 0.902 with thedifterencing length of k = 5.

Note that leverage at the end of year r - A- is determined by the followingequation:

112) Lí,_É = (1 -'y)Li,-k-\

Subtracting equation (12) from equation (8), we obtain

(13) Li,-Li,-k = (I

or

(14) AL¡,,,-k

The long differencing technique estimates equation (14) with iterated two-stageleast squares (2SLS) (see Appendix B for details).

In Figure 5, we show the results of simulations that demonstrate the mag-nitude of the bias in the estimated SOA when either i) a pooled OLS estimatorignoring firm fixed effects is used, ii) a mean differencing (or within-group)estimator is used, or iii) a long differencing estimator is used. The data-generatingprocess is given by

(15) L¡, - (1 -7)Li ,_ ,+7TL, + £~„

where L,,, - NORMAL(0.25,().25), TL, - NORMALiO.25,0.25), and £„ -NORMAL(0,0.1). The simulations are repeated 10,000 limes, each time using1.000 firms and 10 years of data for each firm. The values plotted are the first-order autoregressive coefficients, so subtracting each from 1.0 gives the SOA. InGraph A, we do not restrict the actual level to be between 0 and 1, whereas inGraph B, we do. Inspection of the graphs shows that this restriction is relativelyunimportant.

The simulations show that without fixed effects, the estimated SOA is biaseddownwards (since the estimated autoregressive parameter is biased upwards), andthat the estimated SOA using a mean differencing estimator is biased upwards,with the bias being especially large for slow true speeds. These results corroborateWelch's (2007) findings. Consistent with Hahn et al. (2007), the long differencingestimator works well even when the autoregressive parameter is close to one.

Therefore, we implement the long differencing technique. We report the re-sults in Table 7.^' Using differencing lengths of it=4, 8. 18. and 28 years. Panel A

-' In unreportecl analy^iis, we did two robustness checks. First, we tried not to include the changesin ihe iiiacrocconomic variables as explanatoiy variables. Second, we excluded firm-year observationswith major mergers and acquisitions and spin-iitïs. The esiimates for the SOA are qualitatively the


FIGURE 5

The Estimated Speed of Adjustment as a Function of the True Speed

Simulations tor Ihe estimated speed ol adjustment (SOA) with i} OLS and no firm fixed effects, ii) the firm fixed effeci'.mean differencing estimalor (also known as the wilhin-group estimator), and iii) the long diHerencing estimator. The vaiue;plotted are the fifst-order autoregressive coefficients, so subtracting each from 1 0 gives the SOA. The da ta-gen eral in gprocess IS given by í_,r = { t - 7)L, ,_ i +-/TL, + e«, where L,() ~ NORMAL(0,25, 0.25). TL, -^ NORMAL(0.25.0.251and e,[ — NORMALjO, 0.1). L is leverage, andTL is target leverage. The simulations are repeated 10.000 times, eachtime using 1,000 (Irms and 10 years of data (d = 8) for eaciilirm.

Graph A. Leverage <0or > t Allowed

m 0.4

-0,2

0.1 0,2 0 3 O.A 0-5 0.6 0 7 0,8 0,9 1

True Value

— T r u e Value - • - OLS Ignoring f i xed Effects - * - Mean Diflerencing - * • - Long Diffefencing

Graph S. 0 < Leverage < I

•02

0,1 0,2 0.3 0,4 0.5 0,6 0.7 Q,8 0.9

True Value

— True Value - • - OLS Ignoring Fixed Effects - • - f^iean Diffarencing - • « - Long Differencing


TABLE 7

Long Differencing Estimation of the Speed of Adjustment toward Target Leverage

Using ifie long differencing technique, we estimate the following equation (see Appendix B for details) usina (irms from1969-2001:

The dependent variable is the change in either book leverage or market leverage Between the end of year ( and the endof year I - ii of firm / (fi = 4, 6, 18, or 28). Book leverage is defined as book debt (items 181 + 10 - 35 - 79) divided byl)ook assets (item 6). Market leverage is defined as book debt divided by market assets (items 181 + 10 - 35 + 25 x 199),X includes lagged firm characterisfics, lagged or current market conditions, and year dummies. Q is the sum of the marketvalue of equity and Ihe book value of debt divided by the book value of assets R&D is the research and developmentoxpense (46) scaled by assets and is set to zero if it is missing, R&DD is a dummy variable that equals one if R&D ismissing and equals zero otherwise CAPEX is the capital expenditure (128), SALE is the log of net sales (12), OIBD is theoperating income before depreciation (13), TANG is Ihe net property, plant, and equipment (8). R&D, CAPEX, OIBD, andTANG are scaled by assets, ERP,_, is the implied market equity risk premium at the end of year 1 - 1 Rm,_ , is thenominal interest rate at the end of year t - 1 minus inflation in year I. DSP,_ i is the default spread at the end of year I - 1rSPr _ 1 is the lerm spread at the end of year f - 1, TAXR, is the statutory corporate tax rate during year ( RGDP, is thereal GDP growth rate during year [. Some year dummies are dropped to avoid multicollinearity. For brevity, the coefficientson year dummies are not reported. The (-statistics use heteroskedastic consistent standard errors, further adjusted forcorreiation across observations of a given firm (White (1980). Rogers (1993)),

Panei A Book LeveraQe

¿vU-i,(-i,-,-3Q,,_i^,_t,_i/1R&DD¡,_1^,_((_,¿lR&Df(_ij_(,_iJCAPEX,f_i^,_(,_,iiSALE/f_i,(_i,_i¿10IBD(,_ij_fc_lJTANG|{_ij_j,_,-1ERP,_, , _ ^ _ ,JRIRi_i^(_/,_i^DSP[_i^,_)t_i-iTSP,_,^,_)t_,JTAXR,j_(,..iRGDP,^(_),Year dummiesN

Panel B, Market Leverage

-iU-,,,-».-,-iO,(-t,r_ii_i_iR&DD|,_ij_j(_,|-JR&D,,_i j _ ) i_ ,JCAPEXj,_i,,_(,_i-ASALE,,_i^,_(,_,.-10IBD,,^),,_^_iJTANGrt_i,[_j,_|-itRP,_i,f_(,_i.iRIR,_i,(_(,_!JDSP(_|^(_(,_,-^TSP,_i j _ ) , _ ,JTAXR,,,_((.ARGDP,,,_„r'ear OummiesN

(1)h =

Coeff,

0.789-0.007- 0 002- 0 0 1 6

0,1080,001

-0,1300.009

- 0 0560,038

-0,839-0,055-0,112-0,049

Yes61,145

0,7770.0050.000

-0.0820,2060,026

-0,131-0.010-0.228

0,128-2.247-0,246-0,464-0,376

Yes61,145

4

t-Siat

221,8-8,7-1,7-0,711,00,7

-15.21.3

-1.20,9

-3,3-0,7-1,9-1 ,5

168 76.50.0

-4.417,018,0

- 1 3 6-1 .2-4,1

2,8-6,9-2,6-6,9-8,9

(2)k =(

Coeff.

0.830-0.006-0,001

0,0130,0680,001

-0.12C0.0110,1680,018

-0,780-0,323-0,181

0185Yes

38,162

0.768- 0 , X 1-0,002-0.116

0,1190,020

-0,1630,0160.0610,145

-4,593-0,141-0,175-0,211

Yes38,162

3

I-Stat.

187,5-6 ,8-0,7

0,56.508

-15,21 73,70,5

-3,0-4 ,2-3.1

4.0

139.7-1 .3-1,3-5 .0

9.517.2

-17,92 21.13,1

-13.6-1,4-2,6-3 ,6

h

Coeff

0.873-0.002

0.0000,0530,092

-0,001- 0 110-0,003

0.070-0,019-0-408-0,095-0,283-0,022

Yes11,002

0,828-0,003

0,000-0.074

0,2270,008

-0,126-0,015- 0 097-0.154-4.119-0,254-0,101-0,447

Yes11,002

(3)= 18

i-Stat

142,4-1,7-0.1

1.34,6

-0 ,6-8,3-0,4

0,5-0,3-0.6-0,5-0 ,8-0,3

103,8-2,3

Q,2-1,5

9,05.6

-8,8-1 ,4-0 ,6-1 ,6-4 ,8-1 ,0-0 ,3-4 .0

¡4)h = 28

Coeff.

0,885- 0 003-0.001-0.066

0.132-0.003-0,076-0.021

0,756-0.294

0,75-1-1,347

0,0860,453

Yes2,099

0.844-0,006-0.001-0,169

0,2340.002

-0,114-0,015

0,380-1,015

-12.3760.168

-0,954-0,286

Yes2,099

t-Stat.

67 0-1 .5-0.1-0 ,9

40-1,7-2,5- 1 4

1,1-0 .8

0,2-1 .0

0.20,9

44,8-2 .3-0 ,2-1 ,9

5.007

-3,2-0,7

0.4-2,5- 2 9

0,1- 1 4-0,4

presents the results using book leverage. The long differencing estimator pro-vides an estimated SOA that is much less sensitive to the time dimension than themean differencing estimator. Depending on the differencing length, the estimated


SOA toward target book leverage varies from 11.5% to 21.1% per year. Panel Bpresents the results for market leverage. Tbe estimated SOA toward target marketleverage varies from 15.6% to 23.2%. In botb panels, tbe sensitivity of tbe esti-mates to tbe differencing length is partly because different firms are examined. Foiregressions with k= 18 or 28, one could argue tbat a firm fixed effect is unlikelyto be invariant for 20 or 30 years. Tbe vast majority of firms used in regressionswith it ^ 8 do not have at least 20 years of data, however, so tbe assumption of atime-invariant firm fixed effect should be a less important issue. Witb A = 8, tbelong differencing estimates of the SOA are 17.0% per year for book debt ratiosand 23.2% per year for market debt ratios.

Intuitively, it seems strange thai tbe SOA is faster with market debt ratiostban witb book debt ratios, given tbat Welcb (2004) demonstrates tbat firms donot actively offset increases in tbe market value of equity caused by stock priceincreases. Perbaps firms whose market debt ratios precipitously increase due to ;istock price decrease either see the stock price recover and remain in the sample, ordrop out of the sample due to financial distress or being taken over. Tbe resultingsample selection bias would create a bias toward estimating a bigb SOA.

Chang and Dasgupta (2009) and Chen and Zhao (2007) also question whetherevidence of mean reversion in debt ratios is conclusive evidence of targeting adebt ratio, rather than just a manifestation of a mechanical relation if firms arcfinancing randomly or semirandomly. Tbe evidence in our Table 4 on tbe securi-ties issuance decision, however, suggests that firms are not financing randomly.Chang and Dasgupta (2009) also show that some of the evidence in tbe actual datacan only be replicated if tbeir simulation samples are modified to accommodatemarket timing behavior.

By comparing tbe data in Tables 6 and 7. we can get estimates of the mag-nitude of tbe biases using OLS without fixed effects and tbe mean differencingmethod, relative to the long differencing estimates. When k ^ 28, the long dif-ferencing estimate of tbe SOA for book debt ratios is 11.5%, wbicb is above tbeTable 6, Panel B, OLS estimate without fixed effects of 9.3% and below the meandifferencing estimate of 19.7%. When k = 28. the long differencing estimate tormarket value of 15.6% is above tbe Table 6, Panel B, OLS estimate without fixedeffects of 11.0% and below the mean differencing estimate of 24.6%. Tbis con-firms that tbe OLS estimates ignoring firm fixed effects understate tbe SOA, whilethe mean differencing estimates overstate the SOA.

To facilitate comparisons, estimates of the SOA in existing empirical studiesof capital structure for U.S. firms are reported in Table 8. Fama and French (2002)and Kayban and Titman (2007) use OLS ignoring firm fixed effects. As discussedearlier, tbese estimates are likely to be biased downwards. Tbe other four paperscontrol for firm fixed effects: Flannery and Rangan (2t}06) use the mean differ-encing (or witbin-group) estimator; Antoniou et al. (2008) and Lemmon et al.(2008) use tbe system GMM estimator; and this paper uses tbe long differenc-ing estimator. As we discussed earlier, tbe mean differencing and system GMMestimates are likely to be biased upwards. Consistent with these predictions, thelong differencing estimates for the SOA are much lower than the mean differenc-ing and the system GMM estimates, and higher than the OLS ignoring firm fixedeffects estimates.


TABLE 8

Estimates of the Speed of Adjustment in Empirical Studies of Capital Structure

Fable 8 reports the eslimated annual speed of adjuslmeni (SOA) toward target leverage per year in existing empiricalstudies of capital structure The annualized numbers from Kayhan and Titman (2007) are compiled as ihe compoundedannual speed that achieves the five-year SOA that they report in their Table 2,41% for book leverage and 35% lor marketleverage (l,e , 0,90^ =0,59, andO.9t7= = 0 65) The eslimate from Antoniou et al (2008) is (or U.S, firms In Iheir Table 5,Half-life is the number of years that the SOA implies for a firm lo move halfway toward ils target capital structure, NA is notavailable

Book Leverage Market Leverage

SOA Half-Life SOA Half-LifeEstimator

Fama and French (2002)

Kayhan and Titman (2007)

nannery and Rangar! (2006)

Antoniou, Guney, and Paudyal (2008}

Lemrrxin, Roberts, and Zender (200B)

This paper

OLS ignoring firrr fixed effects tO%^ 6,6 years 7%^ 9 6 yearst8%° 3 5 years 15%" 4.3 years

OLS ignoring lirm fixed effects

Fimi fixed effects, mean differencingestimator with an instrumental variable

Firm fixed effects, system GMM NA

Firm fixed effects, system GMfUl 25%

Firm fixed effects, iong differencing 17%estimator

10% 6,6 years 8,3% 8,0 years

34,2% 1,7years 35,5% t,6years

NA 32,2% 1,8 years

2,4 years NA HA

3,7 years 23.2% 2,6 years

•'Dividend-paying firms.'•"Firms that do not pay dividends

VI. Conclusion

The pecking order theory predicts that external equity is used as the lastresort. Under the market timing theory, equity issues are not necessarily more ex-pensive than debt issues when the equity risk premium (ERP) is low. Furthermore,firms may want to raise funds when the cost of equity is low in order to build a,stockpile of internal funds. Consistent with the market timing theory, we iind thatfirms fund a larger proportion of their financing deficit with net external equitywhen the expected ERP is lower.

When we estimate leverage regressions, we find that historical ERPs havelong-lasting effects on leverage through their influence on securities issuance de-cisions, even after controlling for firm characteristics that have been identified asIhe most important determinants of capital structure. When a Hrm funds a smallerproportion of its financing deficit with debt, which occurs when the market ERPis lower, leverage is lowered for many subsequent years, with the impact gradu-ally diminishing over time. This finding provides further support for the markettiming theory.

We also reconcile the different findings on the speed of adjustment (SOA)toward target leverage In Fama and French (2002), Kayhan and Titman (2007),Flannery and Rangan (2006), Antoniou, Guney. and Paudyal (2008). and Lemmon,Roberts, and Zender (2008). Flannery and Rangan (2006), using a mean differ-encing estimator, and Antoniou et al. (2008) and Lemmon et al. (2008), using asystem GMM estimator, find a much faster SOA toward a target capital structurethan do Fama and French (2002) and Kayhan and Titman (2007), who use OLSwithout firm fixed effects. All three of ihe methods used are biased when some ofthe firms in the data set are present for a small number of years and when leverageis highly persistent. The quantitative extent of the biases can be large.


We reduce the biases due to a short time dimension and a highly persistentdependent variable by instead using the long differencing procedure introducedby Hahn, Hausman. and Kuersteiner (2007). They show that this estimator ismuch less biased than conventional GMM estimators for a dynamic panel, es-pecially when the dependent variable is highly persistent. The application of thisnew technique to our data suggests that fimis adjust slowly tovtard their targetleverage. Using a differencing length of A' = 8. we estimate an SOA of 17.0% peryear for book leverage and 23.2% per year for market leverage. These numbersimply a half-life of 3.7 and 2.6 years, respectively, to remove the effect of a shockto target capital structure.

Our estimates of the SOA toward target debt ratios suggest that firms domove toward target debt ratios, although at a moderate pace. Our evidence impliesthat both the market timing model and the static trade-off model are importanideterminants of capital structure. In periods when the eost of equity is high, suchas 1974-1981. firms act as if they follow a pecking order model with a strictpreference for debt when external financing is needed. In periods when the costof equity is lower, however, the pecking order model fails as a descriptive modelof how firms behave.

The long differencing estimator has far-reaching implications extending be-yond capital structure research. Existing empirical studies of corporate payout andinvestment policies using dynamic models suffer from a similar short time dimen-sion bias. A long differencing estimation of such models would shed lighi on is-sues such as how much earnings firms pay out to shareholders, how quickly firmsadjust toward a long-term target payout ratio, and why firms smooth dividends.

Appendix A. The Residual Income Model

Following Ritter and Warr (2002). we use the following model to estimate the realcost of equity for each stock in the Dow. This approach extends the basic residual incomemodel to correct for inflation-induced distortions:

^ ^ ^ + p , D , - D A , - r x R e B ,I I +7.7,1

V, =(1+r)

FEPS,+2 p,*\D,^\ _ rjA _ ^ X ReB,*i

{\ + p,^i){\ + p,)

FEPS„.i p,+2D,+2 ^ . r X

where V, = Ihe value per share of the firm's equity at time i,ReB, = the replacement book equity per share at time /,

= the / + i earnings per share forecast for the period ending / + /.p, = the expected rate of inflation at time f.D, = the value per share of the firm's debt at lime i,

DA, = the depreciation adjustment at time /.r = the real cost of equity, andg = the real rate of growth of ihe economic value added (EVA).


ReB, is book equity per share at time i adjusted for the effects of inflation on histor-ical cost depreciation, as defined by Ritter and W:UT ((2002), p. 42). We use the one-year-ahead forecast (FEPS,*i) and the two-years-ahead forecast (FEPS,+2) from IBES or ValueLine. The three-years-ahead foreca.st {FEPSf+3) is calculated as FEPS,+: x LTG. whereLTG is the LTG rate from IBES or Value Line. If LTG is missing, we cotnpute FEPS,.»! asfFEPS,+2)^/FEPS,>i. We use the quarterly prediction of the next year's GDP deflator fromIhe Survey of Professional Forecasters to compute the expected rate of inflation. Depreci-ation adjustment. DA,, is computed as Depreciation Expense x [GDP,/fGDP,_„/;) - I].where GDP, = the level of the GDP deflator at time /. and n/2 is an estimate ot half thedepreciable life of the asset.s. We rely on the clean surplus relation to compute future bookvalues per share: ß,ti = ß, + EPS,+i - DIV,^,. where EPS,.n = earnings per share at f -i-litnd DIV,. i = dividend per share at í -)-1. Following Ritter and Warr (2002), we use a valueof g o f -10% per year, representing a decay rate of residual earnings of 10% per year (seeRitter and Warr (2002) for additional details).

We then calcúlale the implied equity risk premium (ERP) as the difference betweenIhe real cost of equity and the expected real rate of return, which is defined as (I +Ihe annuali/ed nominal rate of return on onc-tiionth T-bills from Ihbotson Associates)/( I + ibrecasted growth rate of GDP deflator) - I.

Appendix B. The Long Differencing Estimator

The long differencing estimator for a dynamic panel is first proposed hy Hahn,Hausman, and Kuersteiner (2007) for a dynamic panel wiih a highly persistent data seriesand a short time dimension. We are interested in the estimation of the following equation;

1B-1) L,, - L ,_i = A{L,,-, - U-k-1) + 5(X/,-1 - Xv-t-1) + ii, - èi,-k

Hahn et al. (2007) suggest that U-k-\ is a valid instrument. Using this instrument, welirsl estimate equation (B-2) with two-stage least squares (2SLS) and obtain the initial\ alues of Ihe estimated coefficients Â and 6. Hahn et al. (2007) suggest that the residualsl-i,-\ - \Li,-2 - oXi,-2, - - . , and Z.,,-* — AZ,,,-t-i - oXi,-i-] are also valid instruments.We then use Li,-k-\ and the residuals as instruments to estimate equation (B-2) with 2SLS.We call this the first iteration. We ihen further iterate this estimation. Hahn et al. (2007)suggest that three iterations are often sufficient. We report the results for the third iterationin Table 7.

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