Misallocation and Financial Frictions: the Role of Long-Term Financing

Transcription

1 Msallocaton and Fnancal Frctons: the Role of Long-Term Fnancng Maros Karabarbouns Federal Reserve Bank of Rchmond Patrck Macnamara Unversty of Manchester February 14, 2016 PRELIMINARY-PLEASE DO NOT CIRCULATE Abstract Ths paper analyzes the effect of fnancal frctons on msallocaton when frms can ssue long-term bonds and can default on ther oblgatons. Our model combnes the endogenous nvestment, frm-fnancng structure of Hennessy and Whted (2007) wth the long-term fnancng model of Hatchondo and Martnez (2009). We show that when nvestment s endogenous and frms ssue long-term debt, productve frms can face as severe borrowng constrants as the low productvty frms. Ths occurs because good frms are more lkely to refnance and hence dlute ther exstng debt oblgatons. A key step of our exercse s that we match the large cross-sectonal dsperson n credt spreads we observe n the data. In our model productvty loss due to msallocaton s about 10% whch s 2.5 tmes hgher compared to a model wth short-term fnancng or exogenous collateral constrants. Keywords: long-term bonds, debt dluton, fnancal frctons, msallocaton Contact nformaton: maros.karabarbouns@rch.frb.org and patrck.macnamara@manchester.ac.uk. Any opnons expressed are those of the authors and do not necessarly reflect those of the Federal Reserve Bank of Rchmond or the Federal Reserve System.

2 1 Introducton A growng lterature assgns productvty dfferences between countres, frms, or establshments to recourse msallocaton. For example, Hseh and Klenow (2009) use data on Chnese and Indan establshments and show that recourse msallocaton accounts for 30-60% of the TFP dfference between these countes and U.S. productvty. The natural queston posed by the same lterature s what are the drvng forces behnd recourse msallocaton. Fnancal frctons seems a natural canddate and has ndeed been the focus of numerous papers (Glchrst, Sm, and Zakrajsek (2012), for example). Nonetheless, n an nfluental paper, Mdrgan and Xu (2014) showed that fnancal frctons cannot generate large effcency losses due to msallocaton. In ther paper, fnancal frctons take the form of exogenous borrowng (collateral) constrants. Frms can accumulate nternal funds over tme n order to grow out of ther borrowng constrant. Snce hgh productvty frms are more lkely to quckly grow out of ther constrant relatve to low productvty frms, msallocaton s lmted. We re-evaluate the effect of fnancal frctons on msallocaton through the lens of a structural model of frm fnancng. In our model, frms borrow usng defaultable bonds and nvest n physcal captal subject to adjustment costs. They also have the opton to rase external equty (Hennessy and Whted (2007)). In ths setup fnancal frctons take the form of bankruptcy losses n the case of default. Due to these losses credtors charge a premum over the rsk-free rate to borrowers wth a relatvely hgher probablty of default. Our nnovaton s the ntroducton of long-duraton bonds wthn ths endogenous nvestment model. Long-duraton bonds are modeled followng Hatchondo and Martnez (2009) and Chatterjee and Eygungor (2012). In partcular, we assume that frms promse a geometrcally declnng sequence of payments to bond-holders. Each perod a bond can mature wth some probablty n whch case the frm pays lenders the prncpal. We show that long-term fnancng can affect substantally the ablty of frms and n partcular whch frms exactly can ssue debt. What matters wth long-term fnancng s the sequence of productvty draws untl the bond matures. Wth suffcently low persstence n productvty, current productvty s a poor predctor of whether the frm wll avod default n the future. Hence, for all frms access to borrowng (and thus nvestment) may be lmted. It turns out that hghly productve frms may face even more severe borrowng constrants. Ths occurs because lenders recognze that good frms may have access to cheap borrowng n the future and may be tempted to dlute exstng debt oblgatons. For these reasons, n our model, frms cannot easly grow out of ther constrants and fnd t hard to fnance ther nvestment. 2

3 We test our model usng frm-level data on daly bond ssuances whch we merge wth data from Compustat. We show that our benchmark model can match well the cross-sectonal dstrbuton of credt spreads we observe n the data. Ths s mportant snce the dsperson n credt spreads can be lnked to the dsperson n the margnal product of captal (Glchrst, Sm, and Zakrajsek (2012)), a key statstc to measure msallocaton. The medan credt spread s 2.8% n our model whle 2.4% n the data. The standard devaton n our model s 1.53% whch s a lttle lower than the 2.17% we see n the data. In sharp contrast, a model wth a one-perod bond generates a degenerate dstrbuton close to zero. We fnd that the TFP loss due to msallocaton s around 10% n our benchmark model. In contrast, a model wth a one perod bond or an exogenous borrowng constrant generates msallocaton around 4.0%. Ths s n most part due to a hgher dsperson n the margnal product of captal: n our benchmark model the dsperson s twce as hgh as n the one perod/exogenous constrant model. Usng as a measure of msallocaton the expected TFP loss a measure whch nets out any dstorton arsng from uncertanty over next perod s productvty we can get even larger dfferences between our benchmark and the one perod model. In partcular, our benchmark model can generate msallocaton around 16 tmes hgher (6.5% versus 0.4%). Our paper hghlghts the role of persstence n productvty for msallocaton. Smlar to Mdrgan and Xu (2014), Moll (2014) notes that a frm can undo fnancal frctons by accumulatng ts nternal funds. If productvty shocks are relatvely persstent then a productve frm can quckly go out of ts constrant. In contrast, f productvty shocks are transtory, fnancal frctons can lead to large losses. Our model strengthens the nsghts n Moll (2014) by stressng the mportance of long-term fnancng. If current productvty s a good predctor of whether the frm wll avod default n the future then credtors mght be less reluctant to lend cheaply to a productve frm. In contrast, f productvty s d then both productve and unproductve frms wll face approxmately the same borrowng cost, as what matters s the ablty to pay the coupon up to the maturty. Our paper s also related wth the work of Khan and Thomas (2013). The authors hghlght the mportance of adjustment costs for msallocaton. Large costs to adjust nvestment mght result to frms not beng able to nvest ther frst-best. We also model adjustment costs and hence ncorporate ths type of mechansm. However, we fnd that wth long-term bonds there s another channel that decreases msallocaton n the presence of adjustment costs. Credtors are reluctant to lend money to frms n fear of debt dluton. If frms face severe adjustment costs then t s less lkely that the frm wll sharply change ts captal (and hence ts borrowng opportuntes) untl the bond matures. So n our framework, adjustment costs can reduce msallocaton n captal. 3

4 2 Model Our model combnes the frm fnancng structure of Hennessy and Whted (2007) wth the long-duraton bonds lterature: Hatchondo and Martnez (2009) and Chatterjee and Eygungor (2012). In ths model frms borrow for two reasons: () nternal funds may be nsuffcent to reach the optmal level of nvestment, () there s a tax beneft assocated wth debt whch makes even unconstraned frms seek debt fnancng. The man cost assocated wth debt fnancng s the deadweght losses that occur n the event of default. 2.1 Frms Frms are perfectly compettve and produce a sngle homogeneous good. The frm s profts are assumed to be π(z, k) = zk α c f, where z s an dosyncratc productvty shock, k s the captal nput, and c f s a fxed operatng cost. The process for dosyncratc productvty follows an AR(1) process: ln z = ρ z ln z + ε where ε s an..d. shock drawn from N(0, σ 2 εz). We denote by F (z z) and f(z z) the cumulatve dstrbuton and probablty densty functons for next perod s productvty z, condtonal on the current productvty z. 2.2 Sources of Fnancng for Investment The frm fnances next perod s captal usng three sources: (1) nternal equty, (2) external equty and (3) debt. Buldng on Hatchondo and Martnez (2009) and Chatterjee and Eygungor (2012), we assume frms ssue bonds that promse a geometrcally declnng sequence of payments. Specfcally, suppose the frm had ssued b unts of a bond n the prevous perod. Each bond wll pay a coupon rate of c and a fracton θ wll mature ths perod. For the θb bonds that mature, the frm pays back the prncpal plus nterest, so that the total payment s (1 + c)θb. For the (1 θ)b bonds that do not mature, the frm only pays the coupon, so that the total payment s c(1 θ)b. The total payment from both s then (θ + c)b. Snce only a fracton θ of exstng bonds mature today, the tomorrow s stock of bonds, b, must satsfy b = (1 θ)b + x b where x b s the new ssuance of bonds. Let q(z, k, b ) be the prce at whch the frm s able to sell these bonds, so that the frm receves q(z, k, b ) [b (1 θ)b]. Ths expresson summa- 4

5 rzes the debt dluton problem present when frms borrow long term. A larger ssuance of bonds b wll lkely demand a hgher credt spread a lower q(z, k, b ) whch decreases the dollar amount of current bonds ssued. However, t also dlutes the current stock of bonds ssued n the past. If bonds mature after one perod (as n Hennessy and Whted (2007)) there s no such trade-off. We descrbe the other ways a frm can fnance nvestment by examnng ts budget constrant. Every perod, the frm starts wth an ntal level of captal, k, and an outstandng stock of long-duraton debt, b. The frm fnances k subject to the followng budget constrant: d + k = e(z, k, b) + q(z, k, b ) [b (1 θ)b] g(k, k ) where d s dvdends, g(k, k ) are the captal adjustment costs whch take the form g(k, k ) = { (φ + 1 1)(k (1 δ)k) + φ 2 2 (1 φ 1 )(k (1 δ)k) + φ 2 2 (k k) 2 k (k k) 2 k f k > (1 δ)k f k < (1 δ)k and e(z, k, b) = π(z, k) T c [π(z, k) δk cb] + (1 δ)k (θ + c)b s the frm s short-term nternal equty. T c [π(z, k) δk cb] denote the corporate ncome taxes. When d > 0, the frm s ssung dvdends to shareholders (and shareholders separately pay the dvdend tax rate τ d ). When d < 0, the frm s rasng funds drectly from shareholders. Ths, however, s costly as shareholders must also pay an equty ssuance cost assumed to be a fracton λ of the amount of equty rased. Λ(d) s a functon whch reflects the equty ssuance cost when d < 0 and the dvdend tax when d > 0: { λd f d < 0 Λ(d) = τ d d f d 0. Therefore, when choosng k, the frm has access to three sources of fundng: (1) longduraton debt (.e., q(z, k, b )(b (1 θ)b)) (2) nternal equty (.e., e(z, k, b)), and (3) external equty (when d < 0). 2.3 Tax System Three taxes are consdered n ths paper. The frst s the tax on nterest ncome. Investors must pay a constant tax rate rate, τ, on nterest ncome. The second tax s that shareholders must pay a flat tax rate, τ d, on dvdends. And fnally, the thrd tax s that frms must pay a tax on ther corporate ncome. The frm s taxable ncome, x, s assumed to be profts mnus 5

6 economc deprecaton and nterest expense: x = π(z, k) δk cb where δ s the deprecaton rate of captal and cb s the nterest n expense. As mentoned, snce nterest expenses are subtracted by taxable ncome, frms have an ncentve to borrow even f they have suffcent nternal funds. Then, gven a taxable ncome of x, the frm s total corporate tax bll s gven by T c (x) x 0 τ c (y)dy where τ c (y) s the margnal corporate ncome tax rate at ncome y. 2.4 Value Functons and Default Decson Every perod after the realzaton of z, the frm can choose whether to default or contnue ts operatons. Value of Default lqudated. Hence If the frm defaults the shareholders receve nothng and the frm s V D = 0 Value of ext The value of ext, V x (z, k, b), s defned to be: V x (z, k, b) = d Λ(d) where d = e(z, k, b) q x (1 θ)b g(k, 0) Therefore, when the frm s forced to ext (exogenously), t dstrbutes to shareholders what s remanng of the frm s nternal equty, after buyng back ts un-matured debt at the prce q x and payng the captal adjustment cost g(k, 0). Value of No Default to the followng program: A frm that does not default chooses k and b optmally accordng { } γ V (z, k, b) = max d Λ(d) + d,k,b 1 + r(1 τ ) E [V nd(z, k, b ), 0] 6

7 subject to d + k = e(z, k, b) + q(z, k, b ) [b (1 θ)b] g(k, k ) e(z, k, b) = π(z, k) T c [π(z, k) δk cb] + (1 δ)k (θ + c)b The parameter γ (0, 1] reflects the extra mpatence of the frm. If the frm chooses not to default, wth probablty η, the frm wll stll ext (exogenously). Therefore, we also defne the value functon V nd (z, k, b ) = (1 η)v (z, k, b ) + ηv x (z, k, b ) where V (z, k, b ) s the value the frm receves f t does not ext, whle V x (z, k, b ) s the value the frm receves f t exts (and does not default). Default Threshold In general, we can defne a threshold, z d (k, b ), such that the frm wll default next perod only for realzatons of productvty z < z d (k, b ). Ths threshold s defned to be the value of dosyncratc productvty, z d, such that the frm s just ndfferent between defaultng and not defaultng: V nd (z d, k, b ) = 0 Consequently, ths default threshold wll depend on the frm s chosen levels of captal k and debt b. 2.5 Bond Prce The frm ssues bonds whch are purchased by rsk-neutral lenders. In our model fnancal frctons take the form of bankruptcy costs. In the case of default, the lender s assumed to pay a bankruptcy cost, B(k ): B(k ) = ψ [(1 δ)k g(k, 0)] Snce defaultng frms are lqudated, the lender then recovers R(z, k ): R(z, k ) = π(z, k ) T c [π(z, k ) δk ] + (1 ψ) [(1 δ)k g(k, 0)] It s well documented that bondholders usually recover only a fracton of lqudated frms. We vew the fracton (1 ψ) as representng ths recovery rate. The lender receves the stock 7

8 of captal remanng after bankruptcy costs, as well as the after-tax profts of the frm. However, consstent wth the US tax code, nterest deductons are ds-allowed n default. The mportance of long-term debt shows up when the frm does not default. In these states, the lender receves (θ+c) for each bond. However, wth long-duraton debt, a fracton (1 θ) of the bonds have not matured, and the value of those bonds tomorrow depends on tomorrow s prce q (z, k, b ) and hence tomorrow s debt ssuance b. The lenders wll take ths nto account when chargng the frm a credt premum. Overall, the prce of the bond, q(z, k, b ) s set to guarantee the lender an expected return equal to the rsk free rate: [ q(z, k, b ) = r b z d (k,b ) 0 R(z, k )f(z z)dz + D(z, k, b ) ] (1) where D(z, k, b ) = z d (k,b ) [θ + c + q (z, k, b )(1 θ)] f(z z)dz and q (z, k, b ) = (1 η)q(z, k (z, k, b ), b (z, k, b )) + ηq x. The frst term nsde the brackets captures the usual payoff to the lender n default states. Ths s the man component drvng the credt spread varatons n one-perod bond models. However, wth long-duraton bonds we also have a dluton component, D(z, k, b ). The key dea n ths expresson s that the current prce q depends on the future prce q, so on the future choces of captal and debt and on the future probablty of default. Hence, the frst component reflects the probablty of default one perod ahead whle the second the probablty of default n all future states untl the bond matures. 2.6 New Entrants To model entry we follow Clement and Palazzo (2016) and Katagr (2014) and assume that there s a fxed pool of potental entrants, where the mass of potental entrants s normalzed to one. Each potental entrant draws an ntal productvty, z, from the cumulatve dstrbuton functon G(z). In the calbraton, ths functon s assumed to be the nvarant dstrbuton for dosyncratc productvty. If the potental entrant chooses to enter, t wll mmedately nvest. However, the frm starts wth no captal and no debt, and therefore does not produce n the perod t enters. After the potental entrant chooses to enter, t pays a fxed entry cost c e. In makng ts entry decson, a potental entrant compares the value t would receve from operatng aganst the total cost of entry. Therefore, potental entrants wll enter f 8

9 and only f V (z, 0, 0) c e. As wth default, we can defne a threshold, z e, such that only potental entrants wth z z e wll choose to enter. Ths threshold s defned to be the value of productvty, z e, such that V (z e, 0, 0) = c e Consequently, there wll be selecton on entry, and only the most productve potental entrants wll choose to enter. 2.7 Alternatve Models Our model features () endogenous default and () long-term fnancng. We hghlght the mportance of both assumptons by consderng two alternatve models. The frst s a model wth an exogenous borrowng (collateral) constrant (named Exogenous Constrant Model). We assume that borrowng s lmted up to a fracton of tomorrow s expected profts and un-deprecated captal: b ψ c + ψ z z + ψ k k. Ths s smlar to the specfcaton n Mdrgan and Xu (2014), wth the addton of a constant. In ths model the bond prce schedule s gven by q(z, k ) = { 1+c 1+r f b ψ c + ψ z z + ψ k k 0 f b > ψ c + ψ z z + ψ k k The second model we consder s a model wth endogenous default but short-term fnancng. Ths model keeps the exact same structure as our benchmark model wth the excepton that θ = 1, The model corresponds closely to Hennessy and Whted (2007). We wll refer to ths model as One-perod Bond Model. 3 Model Analyss The magntude of msallocaton refers to the ablty of productve frms to rase funds and undertake ther desred nvestment. In ths secton we dscuss how the presence of longterm fnancng affects the allocaton of resources between productve and unproductve frms. Optmal Fnancng and Investment Polcy: We start our analyss by explanng what determnes the frm s optmal fnancng and nvestment polces. The frst order condtons 9

10 for k and b are [ β V k (z, k, b )h(z z)dz = (1 Λ (d)) 1 q k (b (1 θ)b) + g(k, ] k ) k z d (1 Λ (d)) b {q(z, k, b )(b (1 θ)b)} = β z d (2) V b (z, k, b )h(z z)dz (3) To characterze the dervatves of the value functon, V k (z, k, b) and V b (z, k, b), we apply the Envelope theorem to obtan: [ V k (s, k, b) = (1 Λ (d)) k {π(s, k) T c [π(s, k) δk cb]} + (1 δ) g(k, ] k ) k V b (s, k, b) = (1 Λ (d)) [cτ c (π(s, k) δk cb) (θ + c) q(s, k, b )(1 θ)] Interpretaton of frst order condton for k : The left-hand sde of Equaton 2 depcts the margnal beneft of the addtonal nvestment, whle the rght-hand sde depcts the margnal cost. Holdng b fxed, the addtonal nvestment decreases dvdends by x = 1 q [b (1 θ)b] + g(k,k ). If the frm s currently ssung dvdends (.e., d > 0), k k shareholders pay a lower dvdend tax. Therefore, the margnal cost to the shareholder of the addtonal nvestment s (1 τ d )x. However, f the frm s currently ssung equty (.e., d < 0), the frm must rase an addtonal x unts of equty. Snce ths s costly, the margnal cost to the shareholder s (1 + λ)x. On the other hand, the margnal beneft to the frm s the ncreased value that shareholders receve tomorrow n non-default states (whch they dscount by β). The margnal ncrease n value tomorrow reflects several thngs. Frst note that ths margnal ncrease n value depends on whether the frm s ssung equty or ssung dvdends tomorrow. If the frm s expected to be n an equty-ssuance regme tomorrow, the margnal beneft wll be hgher. The margnal beneft wll reflect the ncreased after-tax profts tomorrow, but wll also reflect the addtonal captal adjustment costs that wll have to be pad tomorrow. Interpretaton of frst order condton for b : At the margn f the frm were to ssue an addtonal bond, t would rase an addtonal x = q + q b [b (1 θ)b] funds from the bond market. If the frm s currently ssung equty (.e., d < 0), ths allows the frm to substtute away from costly external equty. The frm s therefore able to reduce ts equty ssuance by x, and also to reduce the equty ssuance cost by λx. Therefore, n ths case, the margnal beneft of the addtonal borrowng s (1 + λ)x. However, f the frm s currently ssung dvdends (.e., d > 0), ths mples that shareholders receve an addtonal x dvdends. However, snce shareholders must pay a tax on those dvdends, the margnal 10

11 beneft s now (1 τ d )x. The margnal cost of the addtonal borrowng s the reduced value n non-default states tomorrow, whch they dscount by β. Ths s reflected n the rght-hand sde of Equaton 3. Ths margnal value V b (s, k, b ) tomorrow reflects several thngs. Frst, the value depends on whether the frm wll be n an equty ssuance regme or dvdend ssung regme tomorrow. Second, the addtonal debt reduces the corporate ncome tax that the frm has to pay tomorrow (ths s reflected n the term ct c). Thrd, the addtonal borrowng ncreases the burden of the debt tomorrow (n non-default states) by θ + c + q(s, k, b )(1 θ), where q(s, k, b ) s the prce of the debt tomorrow. Long-term debt and nvestment: We show how long-term debt can exacerbate fnancal frctons and affect the frms nvestment choce causng msallocaton. Wy smplfy the frst order condton for k by assumng (1) that there are no taxes (.e., τ d = τ = τ c = 0), (2) equty ssuance costs are zero (.e, λ = 0), (3) there are no captal adjustment costs (.e., g(k, k ) = 0) and (4) γ = 1. In ths case, the frst order condton for k becomes [ ] π(z, k ) E k z = r + δ + z d 0 z d [ π(z, k ) ] + 1 δ h(z z)dz (1 + r) q k [b (1 θ)b] 0 } k {{ } W =wedge [ π(z,k ) k The wedge represents ] the effect of fnancal frctons on nvestment. The term + 1 δ h(z z)dz s assocated wth the probablty of default. If frms default then they wll lose ther nvestment. The term (1 + r) q k [b (1 θ)b] s assocated wth the lnk between the frm s nvestment and the credt spread t pays to the lenders. To understand why long-term debt can affect the optmal nvestment and msallocaton consder the case where b 0. In ths case z d = 0 snce there s no reason the frm would choose to default (and lose ts captal/profts) next perod. If θ = 1 then captal k would be chosen at the pont where the expected margnal product of captal equals r + δ. Implct n ths argument s that the equty ssuance costs are zero so that even low nternal fund frms can nvest ther frst-best level. In such a case the wedge s zero. However, when θ < 1, n spte of b margnal product of captal and r + δ. 0, there s a wedge between the expected The wedge s related to the frm beng able to affect ts credt spreads through nvestment and hence affect ts outstandng debt b. For ths reason (and as we wll show later n the quanttatve analyss), the credt spreads wll always start from a hgher level wth long-term fnancng relatve to a one-perod bond. Fnancal Frctons and Msallocaton: We explot the frst order condton for captal to lnk msallocaton and fnancal frctons. We have shown that we can smplfy the frst 11

12 order condton for captal to [ ] π(z, k ) E k z = r + δ + W where W represent the wedge assocated wth fnancal frctons. heterogeneous across frms but constant over tme (z = z) we have that k = [ r + δ + W az ] 1 a 1 Assumng the z s Aggregate TFP s defned as T F P = Y K a where Y s aggregate output and K s aggregate captal. To measure aggregate output Y we aggregate over all frms output y captal Y = y = z k a = c z 1 1 a [r + δ + W ] a a 1 where c = [ 1 a ] a a 1. Smlarly we aggregate over ndvdual frms captal k to fnd aggregate K = k = c 1 a z 1 1 a [r + δ + W ] 1 a 1 As a result we can wrte total factor productvty as T F P = z 1 1 a [r + δ + W ] a a 1 [ z 1 1 a [r + δ + W ] 1 a 1 ] a The three statstcs that wll affect T F P s the dsperson n productvty σ z, the dsperson n the wedge σ W (whch wll affect the dsperson n the MPK) and fnally the covarance between the productvty and the wedge Cov(z, W ). Note that the lterature assumes jont log-normalty between these random varables so that the covarance drops out. However n our case ths wll not be the case whch wll have mplcatons on msallocaton. Intutvely, f hgh productvty frms can easly access the borrowng market, they wll face a smaller wedge (negatve covarance). In ths case msallocaton wll be lmted. If hgh productvty frms face severe borrowng constrants then the covarance wll be postve and msallocaton wll be larger. 12

13 4 Emprcal Analyss The purpose of ths secton s to present some stylzed facts regardng corporate bond ssuance, credt spreads, nvestment and fnancal characterstcs. We wll focus on the cross-secton of frms. We wll use these cross-sectonal patterns to dscplne and test our quanttatve model. To construct stylzed facts on corporate bond ssuance and nvestment we combne two frm-level datasets. The frst s the Thomson-Reuters... Ths data ncludes daly nformaton on prmary ssuances of corporate bonds. In partcular, the data provde nformaton (among others) on the name of the frm ssung the bond, the amount rased from the deal, the ssue date, the type and purpose of the bond ssuance, the maturty of the bond and the spread over a smlar maturty T-Bll. Table?? reports summary statstcs for corporate bond ssuance, for the perod between The total number of bond deals s 18,728. The average amount rased n a bond deal s $196.2 mllon. To compute the average we weght each deal by ts amount relatve to the total amount ssued n the gven year. Moreover, we fnd that the average bond deal matures n 11.4 years wth a standard devaton of 8.2 years. Ths means that the majorty of bond fnancng nvolves long-term ssuances. The Table also reports the average credt spread of a deal whch s the spread over a T-Bll of a smlar maturty. The average credt spread s around 2.5%. but there s substantal dsperson: the standard devaton s 2.1%. To understand better the large dsperson n credt spreads we also plot the credt spread dstrbuton. Table 1: Bond Deals (Table) and Credt Spread Dstrbuton (Fgure) Bond Deal Statstcs (Average and Standard Devaton) Amount ($Mllons) (189.0) Maturty (Years) 11.4 (8.2) Credt Spread (over T-Bll) 2.5% (2.1%) # Deals 18, Credt Spread (n p.p) Note: The Table reports summary statstcs for Bond Deals for the perod dstrbuton over the same perod. Source: Thomson-Reuters. The Fgure plots the credt spread Usng the dstrbuton of bond deals we construct an expected default rate of corporate 13

14 Table 2: Summary Statstcs: Sales and Investment Statstc Mean St. Devaton Persstence n log-sales Investment Rate < 1% (nacton) 0.08 > 20% (spke) 0.15 Note: The Table reports summary statstcs regardng persstence n log-sales and nvestment rates. Source: Compustat ( ). bonds. In partcular, more than half of the frms/bonds deals are rated by Moody s. As an example, n our sample, 20% of bond deals are rated as A1, 15% as Baa1, 12% as Baa2, and 10% as A3. We use Moody s estmates on default probabltes of each class of bonds to measure an average default rate. We choose the probablty of defaultng after 12 years snce ths s the average maturty n our sample. We fnd that the average default rate of bonds n our sample s 1.56%. The second frm-level dataset s Compustat whch ncludes fnancal nformaton on publcly-held companes. We exclude fnancal frms and utltes as these ndustres are more heavly regulated. We also exclude frms affected by a merger or an acquston. We are left wth 138,018 frm/year observatons. We use ths sample to estmate two set of statstcs. The frst s the persstence n sales. We wll use ths moment to dscplne the productvty process n the model. In partcular, we estmate a frst-order autoregressve process for frm-level log-sales. We control for the year and the frm ndustry. The persstence n log-sales equals 0.81 whle the standard devaton equal to We defne the nvestment rate as nvestment funds used for addtons to property, plants and equpment dvded by total assets. We defne the Inacton regon as an nvestment rate less than 1%. We fnd that around 8% belong to ths group. We defne a Spke n nvestment f the nvestment s above 20% whch corresponds to the 90 th percentle n our data. We fnd that around 15% belong to ths group. The average nvestment rate s 7.4% and the standard devaton s 8.0%. When we merge Compustat wth our bond ssuance dataset we are left wth 5,320 bond deal observatons. The average amount rased n ths subsample s $236 mllon substantally larger than the average amount ncludng all bond deal. Ths s not surpsng as Compustat frms are publcly lsted, typcally large frms that can rase a larger amount of funds f they decde to borrow n the bond market. However, the average maturty and credt spread 14

15 Table 3: Log Credt Spreads and Leverage: Regresson (Table) and Scatterplot (Fgure) (1) (2) (3) Coef./SE Coef./SE Coef./SE 1.99*** 1.87*** 0.49*** Leverage (0.06) (0.05) (0.06) Year F.E. No Yes Yes Controls No No Yes Adj-R Observatons Log Credt Spreads Leverage Note: The Table reports the estmates of a regresson of log-credt spreads on leverage. The Fgure s a scatter plot of log-credt spread and leverage. Source: Thomson-Reuters/Compustat. are not substantally dfferent. For Compustat frms the average bond deal matures n 10.8 years (relatve to 11.4 n the whole sample) whle the average credt spread s around 2.3% (relatve to 2.5% n the whole sample). We next analyze the relatonshp between credt spreads and frm leverage. We merge our bond ssuance data wth data on fnancal statements by Compustat. We defne leverage as debt over assets. Total assets s the book value of assets (data tem #6). We defne debt as the sum of debt n current labltes (data tem #34) and long-term debt (data tem #9). The average leverage rato s 0.28 n the data. We plot the relatonshp between log-credt spread and leverage n Fgure 1. There s a strong postve relatonshp between the two varables. Frms that have hgher leverage are asked to pay a premum when they borrow. To evaluate better ths relatonshp we run the followng regresson: log Credt Spread jt = β 0 + β 1 Leverage jt + D t + Γ jt + ε jt Credt Spread t s the spread pad for a deal by frm j n perod t. Leverage jt s the leverage of frm j n perod t. D t are year dummes. Γ jt s a set of frm and bond controls. As frm controls we nclude the frm ratng by Moody and the frm s ndustry. As bond controls we nclude the amount ssued, the bond maturty. We run the regresson separately wth and wthout controls n Table 2. All specfcatons the relatonshp s postve and sgnfcant. When we nclude both year dummes and frm/bond controls the coeffcent s Ths means that f a frm ncreases ts leverage by 1 percentage pont t wll pay 0.57% hgher n credt spread. 15

16 5 Calbraton In ths secton we descrbe the parameter values and our calbraton strategy. One set of parameters are set externally based on values commonly set n the lterature. Another set of parameters wll be nternally calbrated based on moments computed n the data. We wll employ several statstcs calculated n the emprcal secton descrbed before. Externally Set Parameters The model s computed at an annual frequency. We normalze the wage rate to 1 and set an annual rsk-free rate of 4%. The deprecaton rate s set at 10%, a value commonly employed n the lterature. We abstract from exogenous ext rate for now and set η = 0, c f = 0. Frms do ext endogenously though due to default. We set the captal share equals α = Ths s equvalent to havng a frm whch employed labor and maxmzes profts: π(s, k) = max[f(s, k, n) wn] n where the producton functon s now f(s, k, n) = s[k α n (1 α) ] ε. We use the values α ε = 0.27, (1 α) ε = 0.6 and ε = 0.87 based on Khan and Thomas (2014) (cte?). In that case we wll have a = α ε (1 (1 α) ε) whch gves a = Substtutng for optmal labor, profts can be wrtten as π = A z k a, where z = s (1/(1 (1 α) ε)) and wage s set to normalze A = 1. We follow Khan and Thomas (2014) (cte?)and use z = s ( 1/(1 (1 alpha) ε and σ es = Ths gves ρ z = 0.659, σ ez = The expected maturty of a bond s t=1 tθ(1 θ)t 1 = 1/θ. Snce the expected maturty n our data s 11.8 we set θ = We set c = r whch s just a normalzaton to ensure the rsk free q = 1. Under ths structure, f b s the number of bonds ssued n perod t, then the promsed payment n p t s equal to p t = (c + θ)(1 θ) t 1 b. However, the promsed payments are exactly the same as ssung [(c + θ)/θ]b zero-coupon bonds. Bankruptcy cost equals ψ = 0.25 based on Arellano, Ba, and Zhang (2012). We also set exogenously the dvdent tax tau d = 0.12 a typcal value n the lterature and the equty ssuance cost λ = based on Hennessy and Whted (2007). We ntend to nternally estmate ths parameter later based on the frequency of equty ssuance n the data. We choose the followng parametrc form for our corporate ncome tax functon: T c = { τ cmn x f x < 0 τ cmax x f x 0 where x = π(z, k) δk cb. As mentoned, deductng nterest payments on debt gves 16

17 an ncentve for frms for postve leverage. Our tax functon exhbts a knk whch s typcal n the lterature. We set τ cmn = 0.2 and τ cmax = Internally Set Parameters We calbrate nternally the remanng parameters based on moments computed n our emprcal secton. We dscplne the patence parameter γ to target the medan credt spread n the data. If the frm dscounts the future at low rates (low γ) then ncentves to default are hgher. Credtors acknowledge ths and charge a hgher credt spread. Fnally, we choose φ 1, φ 2 to match (1) the frequency of frms n the nacton regon ( /k < 1% ) and (2) the cross-sectonal standard devaton of nvestment rates. 6 Quanttatve Analyss We descrbe n ths secton the basc quanttatve propertes of our model. We focus on how the credt spreads (bond prce schedule) are affected by changes n productvty. Probablty of Default: Short vs. Long Horzon The hgher the probablty of default the hgher credt spread charged by the credtors. To understand how long-term fnancng affects the credt spread we plot n Fgure 1 the probablty of default as a functon of b. In our long-term framework each frm can ssue a bond whch matures each perod wth probablty θ. Hence, we can dstngush between the probablty of default n the short-run (next couple of perods, for example) from the probablty of default over a longer horzon (10 years ahead). Fgure 1 makes ths dstncton. Note that n the one-perod bond model (Hennessy and Whted (2007)) only the left panel s n effect as the bond matures wth probablty θ = 1 after 1 perod. In all horzons the default probablty ncreases wth a hgher debt ssuance b. A hghly ndebted frm wll have smaller value and hence wll fnd default more attractve. More noteworthy s the relaton between productvty and default probablty. Intutvely, a more productve frm wll nvest more so that default wll become less attractve. At the same tme, a (currently) productve frm can fnd easy access to future credt and mght be more lkely to end up n defaultng states n the future. Implct n ths argument s a relatvely low persstence n the productvty process. Whle the former channel s always n effect, the latter s true only for the case of a long-term fnancng. Indeed, we see that the default probablty decreases n z when the bond matures after one perod. In ths case, current productvty s a good predctor of whether the frm wll default n the next perod. However, as the tme-horzon of the bond grows a productve frm mght face a hgher probablty of default. 17

18 Fgure 1: Probablty of Default perod ahead Low prod. Hgh prod perods ahead perods ahead Default Probablty b prme b prme b prme Note: Ths fgure plots the probablty of default across b and z for dfferent tme horzons: 1-perod, 5-perod, and 10-perod ahead. The one-perod case s equvalent to θ = 1. Bond Prce Schedule The next step s to examne how the bond prce schedule q(z, k, b ) s determned n the presence of long-term bonds. Ths s mportant as the dsperson of credt spread dstrbuton wll matter for the dsperson n the margnal product of captal. Fgure 2 plots the bond prce schedule aganst b for the case of a one-perod bond θ = 1 and for our long-term bond model θ = We plot the schedule for several values of z. Wth long-duraton the bond prce schedule dffers substantally from the one-perod bond. Frst, for low values of debt, the bond prce starts out at a value less than 1. Ths means that credtors wll charge a premum even for low amounts of debt ssuance. In the one-perod bond model, frms can ssue a small amount of debt at the rsk-free prce, whch s normalzed to 1 n ths model. Second, long-term maturty affects the slope of the bond prce schedule. In the one-perod bond credtors allow the frm to borrow at the rsk-free rate up to some amount, after whch they sharply ncrease the credt spread (q falls steeply). In our benchmark model, the slope of the bond prce falls (n some but not all cases) more gradually. Moreover, the borrowng capacty of a frm s more lmted n the long-duraton bond case, as q falls to zero for much lower values of b. Therefore, there are two channels through whch long-duraton debt wll generate credt spreads n equlbrum. The frst s through the effect of the ntal bond prce as b approaches 18

19 Fgure 2: Bond Prce Schedule Bond prce, θ=1 Bond prce, θ= q q Low prod. Medum prod. Hgh prod b prme b prme Note: Ths fgure plots the bond prce schedule across b and z for θ = 1 (Left Panel) θ = (Rght Panel) zero. The second s through the effect of long-duraton debt on the slope of q(z, k, b ). To understand why long-duraton debt nfluences the bond prce n these ways, t s useful to analyze the bond prcng equaton defned n Equaton 1 (repeated here for convenence): where D(z, k, b ) = [ q(z, k, b ) = 1 ] 1 z d R(z, k ) + D(z, k, b )f(z z)dz 1 + r b 0 z d [θ + c + q (z, k (z, k, b ), b (z, k, b ))(1 θ)] f(z z)dz. As mentoned, f b 0 then z d = 0 whch further mples that q(z, k, b ) = D(z, k, b )/(1 + r). When θ = 1, D(z, k, b ) = 1 + c, and therefore q = 1 (snce we assume c = r). However, when θ < 1, today s bond prce may be less than one f tomorrow s bond prce q s expected to be less than one. Therefore, even though the probablty of default s zero, the frm stll pays a premum for ts debt because of the possblty that the 19

20 frm wll make future nvestment and debt decsons whch wll lower the value of un-matured debt ssued today. The shape of the default probabltes (Fgure 1) help us understand the slope of q. In the one-perod bond case the default probablty rses sharply toward one, once the frm exceeds a b threshold. As a result, q declnes sharply toward zero. In the long-term bond case, q wll reflect the probablty of default over many horzons. As b ncreases more and more defaultng states wll become lkely whch wll gradually decrease q. The relaton between default probabltes and productvty help us analyze the relaton between the bond prce schedule (Fgure 1) and productvty. For productve frms (that undertake hgh nvestments) the probablty of default one perod ahead s lower. Ths happens because the frm wll not wsh to lose ts captal. However, f the frm can ssue new debt n the future then lenders wll take ths nto account when chargng the frm a premum. It turns out that hgh z frms wll be more lkely to borrow excessvely n the future (.e. choose a hgh b, b etc.) snce they wll able to refnance ther debt relatvely cheaply. Ths wll make these frms more prone to fnancal dstress relatve to low z who wll not be able to fnd easy access to credt. 7 Results 7.1 Credt Spreads We report n Table 4 some statstcs from our benchmark model and compare them to the data. We also compare our benchmark to a model wth a one-perod bond (θ = 1) and an exogenous collateral constrant. Our model captures the medan credt spreads n the data (2.8% vs. 2.4%). In contrast, n the one-perod bond model the medan credt spread s very low compared to the data. The benchmark also captures better the wde dsperson n the credt spreads. The standard devaton of credt spreads s 1.5% n our model versus 2.17% n the data. The one-perod bond model msses the dsperson by a wde margn (0.07%). Fgure 3 plots the credt spread dstrbuton for the data, the benchmark model and the one-perod bond. As mentoned, our model can generate substantal dsperson n the credt spreads close to the one n the data. The shape of the dstrbutons s related to the bond prce schedules (Fgure 2). In the one perod bond model the bond prce falls very steeply after a b threshold. Ths makes all frms choosng a b so that they pay a rate approxmately equal to the rsk-free rate. In the long-term bond case the bond prce schedules () start from dfferent ntal ponts, dependng on productvty and () decrease more gradual, whch allows a wder dsperson n the credt spreads. 20

21 Fgure 3: Credt Spread Dstrbutons Note: The top panel plots the equlbrum dstrbuton of credt spreads when θ = 1. The mddle panel plots the credt spread dstrbuton when θ = 1/11.8. The bottom panel shows the data from Thompson-Reuters. Table 4: Model Statstcs Moment Data Benchmark One-perod Bond Exogenous Targeted Moments Medan Credt Spread 2.4% 2.8% 0.03% 0% Untargeted Moments St. Dev. of Credt Spread 2.1% 1.5% 0.06% 0% Average Default Rate 1.5% 4.3% 0.07% 0% 21

22 7.2 Calculatng Msallocaton We descrbe here how we compute TFP losses that arse due to the msallocaton of captal and labor across frms. We provde more detals of the dervatons n the Appendx. To compute TFP losses, we take as gven the total stock of captal K = kdµ and the total stock of labor N = ndµ n the economy. We then allocate captal and labor across frms to maxmze total output, subject to the constrant that the same amount of aggregate captal and labor are used as n the orgnal economy. In other words, takng as gven the aggregate stock of captal K and labor N from the orgnal economy, we solve the followng problem: max k,n s k ˆα n ˆβ subject to k = K n = N The soluton to ths problem requres that the margnal product of captal and the margnal product of labor are equated across frms. In ths case, the effcent level of output wll be gven by Y e = Γ 1 ˆα ˆβK ˆα N ˆβ where Γ = s1/(). Γ 1 ˆα ˆβ s the effcent level of TFP. We can derve the frst-order condtons ˆαs k ˆα 1 n ˆβ = λ k (4) ˆβs k ˆα n ˆβ 1 = (5) where λ k, are the Lagrange multplers assocated wth the two constrants. Therefore, the margnal product of captal and the margnal product of labor needs to be equated across frms. After some dervatons (see Appendx) aggregate output can be decomposed as: ( s (w k ) ˆα (w n ) ˆβ ) 1/() Y = K ˆα N ˆβ } Γ {{} T F P Γ 1 ˆα ˆγ 22

23 where w k represents the wedge between the margnal product of captal and λ k for frm, whle w n represents the wedge between the margnal product of labor and. If w k = 1, w n = 1, then Y = Γ 1 ˆα ˆβK ˆα N ˆβ. In other words, ths s the case when λ k = r + δ and = w. In our framework nvestment decsons k are taken a perod before productvty z s realzed. Wth suffcently low persstence t s possble that captal s msallocated due to uncertanty over z. For ths reason we construct an expected measure of TFP loss. In ths calculaton, we reallocate captal and labor across frms to maxmze the expected level of output. That s, we take as gven the stock of captal K = k dµ and next perod s stock of labor N = E[n (s )]dµ. We then allocate captal and labor across frms to maxmze total expected output, subject to the constrant that the same amount of aggregate captal and labor are used as n the orgnal equlbrum. In other words, takng as gven K and N from the orgnal economy, we solve the followng problem: max E [s (k )ˆα (n (s )) ˆβ s ] k,n (s ) subject to k = K E[n (s ) s ] = N In other words, for each frm we choose next perod s captal k, and a rule for labor tomorrow n (s ) as a functon of the realzed value of productvty, s, to maxmze expected aggregate output. The soluton to ths problem wll requre that the expected margnal product of captal be equated across frms, and that the margnal product of labor s equated across frms as well. In ths case, the effcent expected level of output wll be gven by E[Y ] = (Γ ) 1 ˆα ˆβ(K )ˆα (N ) ˆβ where Γ E[(s ) 1/(1 ˆβ) s ] (1 ˆβ)/(). (Γ ) 1 ˆα ˆβ s the effcent expected level of TFP. The frst order condtons are λ k = E [ˆαs (k )ˆα 1 n (s ) ˆβ s ] (6) = ˆβs (k )ˆα n (s ) ˆβ 1 (7) The expected margnal product of captal needs to be equated across frms, whle the 23

24 Fgure 4: Smulated Margnal Product of Captal vs Productvty Note: Ths fgure plots the smulated margnal product of captal aganst productvty for θ = 1 and θ = 1/11.8. margnal product of labor s equated across frms. After some calculatons we can derve the total expected output whch s ( K E[y s )ˆα ( N ] = Γ Γ ) ˆβ 7.3 TFP losses from Msallocaton E [(s ) 1/(1 ˆβ) s ] ˆ 1 ˆβ/() We focus on two summary statstcs that can affect msallocaton. Frst, the standard devaton of margnal product of captal and second the correlaton between margnal product of captal and productvty. To get a sense about these statstcs, Fgure 4 plots the smulated values of the margnal product of captal versus productvty. In the benchmark model the dsperson of MPK as well as the correlaton between MPK and z are hgher than n the one perod bond model. In Table 5, we report the TFP loss n all models: benchmark, one-perod bond and exogenous borrowng constrant as well as a model where all knd of frctons have been shut down. We report the TFP loss and the expected TFP loss as derved n the prevous secton. 24

25 Table 5: Msallocaton Statstcs TFP loss Benchmark One-Perod Exogenous Borrowng No Frctons Bond Model Constrant Model All frms 9.9% 4.0% 4.1% 3.5% Bottom 95% n CS 3.6% 4.0% 4.1% 3.5% Standard Devaton of MPK All frms 10.5% 4.9% 4.9% 4.2% Bottom 95% n CS 9.0% 4.0% 4.1% 3.5% Corr(log MP K, log z) All frms Bottom 95% n CS Expected TFP loss All frms 6.5% 0.4% 0.5% 0.0% Bottom 95% n CS 1.0% 0.4% 0.5% 0.0% Standard Devaton of MPK All frms 17.5% 3.9% 4.2% 0.0% Bottom 95% n CS 12.5% 3.9% 4.2% 0.0% Corr(log MP K, log z) All frms Bottom 95% n CS Note: We report the TFP loss n all models: benchmark, one-perod bond and exogenous borrowng constrant. We also report separately the standard devaton of MPK and the correlaton between MPK and productvty. In our benchmark model there s small fracton of frms that s dlutng ts debt s facng very hgh credt spreads. We thus separate our results further between all frms and frms n the bottom 95% of credt spread dstrbuton. Msallocaton amounts to 9.9% TFP loss n our benchmark model as opposed to around 4.0% n the one-perod model and the exogenous constrant model. If there are no frctons msallocaton results to 3.5% loss whch stems from frms makng nvestment decsons before knowng next perod s productvty. Hence, expected TFP loss from msallocaton s 0.0% for the case wth no frctons. In ths case, the loss s 6.5% for our benchmark and around 0.5% for the one-perod model and the exogenous constrant model. In sum, our long-term fnancng model generates msallocaton between 2.5 and 13 tmes hgher relatve to a one perod bond model (or an exogenous constrant model). To understand ths result we can compare the standard devaton of MKP between these models. In our benchmark model the standard devaton s 10.5% as opposed to 4.9% n the other two 25

26 models. However, the correlaton between MPK and z s a lttle lower n the benchmark than the other two models but only f we nclude the top 5% frms n the credt spread dstrbuton. But the ncrease n the dsperson of MPK more than compensates the declne n the correlaton (for all frms) so that the TFP loss ncrease overall. 8 Concluson We analyze the effect of fnancal frctons on msallocaton n a model wth long-term fnancng and endogenous nvestment. We show that our model can generate substantally larger dsperson n the margnal product of captal as well as larger correlaton between productvty and margnal product of captal. In our setup productve frms may face hgher credt spreads snce they can easly refnance and hence dlute ther current debt oblgatons. We fnd that msallocaton s 3 tmes hgher n our model compared to a model wth a one-perod bond or an exogenous collateral constrant. We conclude that the ntroducton of long-term fnancng (coupled wth endogenous nvestment) s crucal to properly account for the effect of fnancal frctons on msallocaton. 26

27 References Arellano, Chrstna, Yan Ba, and Jng Zhang Frm Dynamcs and Fnancal Development. Journal of Monetary Economcs 59 (6): Chatterjee, Satyajt and Burcu Eygungor Maturty, Indebtedness, and Default Rsk. Amercan Economc Revew 102 (6): Clement, Gan Luca and Berardno Palazzo Entry, Ext, Frm Dynamcs, and Aggregate Fluctuatons. Amercan Economc Journal: Macroeconomcs 8 (3):1 41. Glchrst, Smon, Jae W. Sm, and Egon Zakrajsek Msallocaton and Fnancal Market Frctons: Some Drect evdence from the dsperson n borrowng costs. Revew of Economc Dynamcs 16 (1): Hatchondo, Juan Carlos and Leonardo Martnez Long-duraton Bonds and Soveregn Defaults. Journal of Internatonal Economcs 79 (1): Hennessy, Chrstopher A. and Ton M. Whted How Costly Is External Fnancng? Evdence from a Structural Estmaton. Journal of Fnance 62 (4): Hseh, Chang-Ta and Peter J. Klenow Msallocaton and Manufacturng TFP n Chna and Inda. Quarterly Journal of Economcs 124 (4): Katagr, Mtsuru A Macroeconomc Approach to Corporate Captal Structure. Journal of Monetary Economcs 66: Khan, Aubhk and Jula K. Thomas Credt shocks and Aggregate Fluctuatons n an Economy wth Producton Heterogenety. Journal of Poltcal Economy 121 (6). Mdrgan, Vrglu and Danel Y Xu Fnance and Msallocaton:Evdene from plantlevel data. Amercan Economc Revew 104 (2): Moll, Benjamn Productvty losses from fnancal frctons:can self-fnancng undo captal msallocaton? Amercan Economc Revew 104 (10):

28 A Appendx A.1 Msallocaton Frst, we compute the sze of TFP losses that arse due to the msallocaton of captal and labor across frms. To compute TFP losses, we take as gven the total stock of captal K = kdµ and the total stock of labor N = ndµ n the economy. We then allocate captal and labor across frms to maxmze total output, subject to the constrant that the same amount of aggregate captal and labor are used as n the orgnal economy. In other words, takng as gven the aggregate stock of captal K and labor N from the orgnal economy, we solve the followng problem: subject to max k,n s k ˆα n ˆβ k = K n = N The soluton to ths problem requres that the margnal product of captal and the margnal product of labor are equated across frms. In ths case, the effcent level of output wll be gven by Y e = Γ 1 ˆα ˆβK ˆα N ˆβ where Γ = s1/(). Γ 1 ˆα ˆβ s the effcent level of TFP. Gven producton functon f(s, k, n) = s [k α n 1 α ] γ = sk ˆα n ˆβ, aggregate output n equlbrum s gven by Y = f(s, k, n(s, k; w))dµ where µ(s, k, b) s the statonary dstrbuton of frms. Solvng f n = w, labor demand s: n d (s, k; w) = ( ) 1/(1 ˆβ) ˆβ ˆα sk w 28