OPTIMAL CAPITAL UTILIZATION BY FINANCIAL FIRMS: EVIDENCE FROM THE PROPERTY-LIABILITY INSURANCE INDUSTRY By J. Davd Cummns* Gregory P. Nn June 29, 2001 J. Davd Cummns* Gregory P. Nn The Wharton School The Wharton School 3641 Locust Walk 3641 Locust Walk Phladelpha, PA 19104 Phladelpha, PA 19104 Phone: 215-898-5644 Phone: 215-898-5644 Fax: 215-898-0310 Fax: 215-898-0310 Emal: cummns@wharton.upenn.edu Emal: greg30@wharton.upenn.edu *Please address correspondence, page proofs, etc. to Davd Cummns.
OPTIMAL CAPITAL UTILIZATION BY FINANCIAL FIRMS: EVIDENCE FROM THE PROPERTY-LIABILITY INSURANCE INDUSTRY Abstract Captalzaton levels n the property-lablty nsurance ndustry have ncreased dramatcally n recent years the captal-to-assets rato rose from 25 percent n 1989 to 35 percent by 1999. Ths paper nvestgates the use of captal by nsurers to provde evdence on whether the captal ncrease represents a legtmate response to changng market condtons or a true neffcency that leads to performance penaltes for nsurers. We estmate best practce techncal, cost, and revenue fronters for a sample of nsurers over the perod 1993-1998, usng data envelopment analyss, a non-parametrc technque. The results ndcate that most nsurers sgnfcantly overutlzed equty captal durng the sample perod. Regresson analyss provdes evdence that captal over-utlzaton prmarly represents an neffcency for whch nsurers ncur sgnfcant revenue penaltes.
1. Introducton Insurers hold equty captal to provde assurance to polcyholders that clams wll be pad f losses are hgher than expected or f nvestment returns fall short of expectatons. The objectve s to attan an optmal level of nsolvency rsk that balances the margnal benefts and costs of holdng equty captal. There are margnal benefts from holdng captal because safer nsurers command hgher prces and because nsurers rsk losng customers f nsolvency rsk s perceved as excessve (Sommer 1996, Cummns and Danzon 1997). However, holdng equty captal n an nsurance company s costly due to regulatory costs, agency costs from unresolved owner-manager and ownerpolcyholder conflcts, the costs of adverse selecton and moral hazard n nsurance underwrtng and clams settlement, corporate ncome taxaton (Cummns and Grace 1994), and other market frctons. Hence, nsurers do not hold suffcent captal to elmnate nsolvency rsk; rather, nsurers mantan market-drven ''safe'' or ''adequate'' levels of captal (Cummns, Grace, and Phllps 1999). 1 A puzzle has developed n the property-lablty nsurance ndustry as captalzaton has rsen to unprecedented levels n recent years. The rato of premums wrtten to surplus, the ndustry's standard leverage ndex, tradtonally fluctuated around two. Begnnng n the md-1980s, however, the rato began a precptous declne and dpped below one at the end of 1999. Lkewse, the equty captal-to-assets rato, tradtonally around 25 percent, ncreased to 35 percent by 1999. These developments rase questons about whether the ndustry s over-captalzed or whether structural changes n the nsurance or captal markets have altered the optmal degree of captalzaton. The objectve of ths paper s to analyze captalzaton n the property-lablty ndustry to provde new evdence on whether nsurers are over-utlzng equty captal. We employ a fronter effcency approach to analyze captal utlzaton of property-lablty nsurers over the perod 1993-1998. Usng data envelopment analyss (DEA), a non-parametrc technque, we estmate ''best 1 Regulaton, ncludng the Natonal Assocaton of Insurance Commssoners (NAIC) rsk-based captal system, specfes mnmum levels of captal for nsurers. However, the vast majorty of nsurers mantan sgnfcantly hgher captal than requred by rsk-based captal rules (see Cummns, Grace, and Phllps 1999). 1
practce'' techncal, cost, and revenue fronters and measure the effcency of each frm n the sample relatve to the fronters, producng estmates of techncal, allocatve, cost, and revenue effcency. A key concept that we use n analyzng nsurer captal utlzaton s that of cost effcency, whch measures the frm's success n mnmzng costs. Cost effcency s defned as the rato of the costs that would be ncurred by a fully effcent frm producng the frm's outputs to the costs actually ncurred by the frm. Thus, fully effcent frms have cost effcences of one, and neffcent frms have cost effcency between zero and one. Cost effcency can be decomposed nto techncal effcency and allocatve effcency. Techncal effcency measures the frm's success n usng stateof-the-art technology,.e., n operatng on the producton fronter. Allocatve effcency measures the frm's success n choosng the cost mnmzng combnaton of nputs, condtonal on output quanttes and nput prces. To be fully cost effcent, a frm must operate wth full techncal and allocatve effcency. We also estmate revenue effcency, whch measures the frm's success n maxmzng revenues. Revenue effcency s defned as the frm's actual revenues dvded by the revenues of a fully effcent frm that utlzes the same quantty of nputs. As wth cost effcency, techncal, allocatve, and revenue effcency equal one for fully effcent frms and are between zero and one for neffcent frms. Lower effcency scores ndcate more neffcent frms. The concept of allocatve effcency provdes a natural way to analyze whether nsurers are under- or over-utlzng captal. Allocatve effcency measures the extent to whch a frm chooses the correct quanttes of nputs n order to produce ther outputs. Further, the estmaton procedure generates estmates of the optmal nput quanttes for each frm n the sample. By comparng the actual captal for a gven frm wth ts optmal captal, we can determne whether the frm s under or over-utlzng captal relatve to the captal that would be used by a fully effcent frm wth the same quantty of outputs. There are two possble reasons why frms may be measured as under- or over-utlzng captal 2
n our DEA analyss. The frst possblty s that measured sub-optmal captal utlzaton represents a ratonal response to market factors or frm characterstcs that legtmately requre dfferental captal utlzaton. If ths explanaton s correct, a frm's performance should not be adversely affected by dfferences between ts actual captal and ts measured optmal captal. The second possble explanaton s that measured under- or over-utlzaton of captal represents a true neffcency that degrades frm performance. To provde nformaton on whch explanaton s correct, we utlze revenue effcency and book-value return on equty (ROE) to measure frm performance and estmate the mpact of captal utlzaton on these performance measures. We regress revenue effcency scores and book-value ROE aganst a set of explanatory varables, ncludng the rato of the frms' actual less optmal captal to assets. Ths rato, whch we call the sub-optmal captal-to-assets rato, represents the amount of captal under- or over-utlzaton relatve to assets. A larger value for ths rato ndcates excessve use of captal relatve to our measured level of optmal captal. If measured sub-optmal captal utlzaton represents neffcency, then we expect the sub-optmal captal to assets rato to have adverse effects on frm performance, as explaned n more detal below. 2 In addton to measurng the effects of sub-optmal captal on frm performance, we specfy and test several hypotheses regardng the characterstcs of frms that are lkely to be assocated wth captal utlzaton. We regress the rato of the frm s actual-to-optmal captal aganst a vector of explanatory varables representng the theoretcal hypotheses. These tests enable us to control for dfferences among frms that may help to explan observed patterns of captal utlzaton n the ndustry. By way of prevew, we fnd that the run-up n equty captal of the past decade s prmarly attrbutable to captal gans on nvestments. Further, we provde evdence that captal levels n the ndustry are ''stcky'' n the sense that nsurers are reluctant to pay out captal accumulatons as 2 We also perform smlar regressons to test f the effect s symmetrc for under and over-utlzaton of captal. By separatng the sub-optmal captal-to-assets rato nto postve and negatve components, we test whether any adverse effects of sub-optmal captal utlzaton dffer dependng upon whether the nsurer s under- or over-captalzed. 3
dvdends, preferrng to mantan nternal funds to cushon the loss or nvestment shocks. Fnally, we fnd that nsurers are substantally over-utlzng equty captal and that the over-utlzaton represents neffcency that leads to sgnfcant revenue and cost of captal penaltes for neffcent frms. The remander of the paper s organzed as follows: Secton 2 provdes an emprcal overvew of captalzaton trends n the property-lablty nsurance ndustry to provde background for the subsequent dscusson. In secton 3, we formulate hypotheses about nsurer captal structure and specfy the varables used to test the hypotheses. Secton 4 dscusses hypotheses and varables regardng revenue effcency and ROE. Secton 5 dscusses our estmaton methodology, and secton 6 descrbes our sample and specfes the nputs and outputs used n the DEA analyss. The results are presented n secton 7, and secton 8 concludes. 2. CAPITALIZATION TRENDS IN PROPERTY-LIABILITY INSURANCE Leverage ratos for the property-lablty nsurance ndustry for the perod 1970-1999 are graphed n Fgure 1. Two leverage ratos are shown - the rato of net premums wrtten to equty captal (surplus) and the equty captal-to-assets rato. The former s the tradtonal leverage rato used n the ndustry, whle the latter s used more commonly n the fnancal nsttutons lterature. Both leverage ratos llustrate that equty captalzaton n the ndustry has ncreased dramatcally over the past ffteen years. The premums-to-surplus rato was near 2.0 n 1985 but then began an almost unnterrupted declne to less than 1.0 by 1999. The captal-to-assets rato, whch stood at 25 percent n 1985, ncreased to 37 percent by 1999. The trends n the leverage ratos are prmarly due to growth n nsurer equty captal. Durng the ten-year perod 1990-1999, equty captal growth averaged 10 percent per year (on a book bass), whle premum growth was only about 3 percent per year. The dvergent growth rates n captal and premums are shown n Fgure 2, whch graphs the sx-year movng averages n the growth rates for these two varables. Except for bref perods such as the md-1980s, the growth rate n captal has far 4
exceeded the growth rate n premums. Durng the 1990s, the captal growth n the ndustry tracks the bullsh stock market (see further dscusson below). What can explan the dramatc changes n captal structure n ths ndustry? There are several possbltes, most of whch are explored n more depth below: (1) The ntroducton of a rsk-based captal (RBC) system by the Natonal Assocaton of Insurance Commssoners (NAIC) n 1994. The ntroducton of the RBC system was wdely antcpated and may have led nsurers to accumulate more captal to reduce the probablty of ncurrng regulatory costs under the new system. (2) The rse n mportance of ratng agences. The nsurance product market s known to react to ratngs downgrades by frms such as the A.M. Best Company, Standard & Poor's, and Moody's. For example, n the commercal lnes market, t s necessary for nsurers to mantan at least an A ratng n order to avod losng customers to compettors. The ratng agences have played a more aggressve role wth respect to nsurers followng the run-up n nsurer nsolvences n the late 1980s and early 1990s. Thus, some nsurers may have accumulated addtonal captal to protect ther fnancal ratngs. (3) The growth n the market for alternatve rsk transfer products, whch provde a substtute for conventonal nsurance. These nclude self-nsurance programs, captve nsurance companes, and securtzed fnancal rsk transfer nstruments. These products have draned many of the more predctable rsks out of nsurance markets, ncreasng the overall volatlty of nsurer lablty portfolos. Addtonally, the rse of the alternatve market has caused premum growth to stagnate, partally accountng for the gap between premum and equty growth. (4) An ncreased awareness by nsurers of ther exposure to catastrophc property losses coupled wth nadequate supply of rensurance for such losses. Followng hurrcane Andrew n 1992 and the Northrdge earthquake n 1994, nsurers revsed upward ther estmates of potental losses due to catastrophes such as hurrcanes and earthquakes. Smultaneously, t became apparent that 5
rensurance for these large events was nadequate (Swss Re 1997, Froot 1999). Thus, nsurers wth sgnfcant catastrophe exposure may have added captal to cushon catastrophc loss shocks. (5) The 1990s bull market n corporate equtes, combned wth nsurer reluctance ncrease stockholder dvdends. There s both theoretcal and emprcal evdence that there s consderable stckness among nsurers n adjustng dvdends n response to ncreases n equty (Wnter 1994, Gron 1994, Cummns and Danzon 1997). The stckness s drven by nformatonal asymmetres that make t dffcult for nsurers to rase captal after a loss or nvestment shock, nducng them to hold onto captal wndfalls n antcpaton of the next underwrtng crss. (6) Agency costs and other aspects of nsurer organzatonal and market structure. These factors, ncludng the role played by mutual nsurers, are dscussed n more detal below. Tracng the source of the ndustry's growth n equty captal may provde some ntal answers to the captal structure puzzle. Table 1 breaks down the ndustry's growth n book equty nto ts sources and uses for the perod 1989-1998. Secton A of the table shows that total captal grew by $215.7 bllon from 1989-1998, net of $78.8 bllon n stockholder dvdends and $29.4 bllon n mscellaneous outflows. These captal dsbursements are added back to the net change n captal to gve the gross change n captal, and secton B of the table shows the percentages of the gross change from each source of captal. Captal gans provded the most mportant source of new captal durng the ten-year perod 1989-1998 and the four-year perod 1995-1998, accountng for 51.7 percent durng the former perod and 57.0 percent durng the latter. The second most mportant source of gross new captal s retaned earnngs (net underwrtng ncome plus nvestment ncome), and the thrd most mportant source s new captal pad-n, from new equty offerngs or contrbutons from parent frms. The uses of the gross changes n equty are shown n secton C of the table. Insurers pad out as dvdends about onefourth of the total gross change n captal whle retanng about two-thrds, wth the remander devoted to mscellaneous uses. 6
Table 1 provdes some support for the captal stckness hypothess,.e., that captal accumulates because nsurers are concerned about the feasblty of rasng new captal followng the next major underwrtng or nvestment shock. The last column n secton A of the table shows the dvdend payout rate over the perod,.e., the rato of stockholder dvdends pad to the total gross change n captal. The average payout rate s sgnfcantly lower n the second half of the sample perod than durng the frst half, even though the second half of the sample perod accounted for about 70 percent of the total change n gross captal. Ths s consstent wth the vew that nsurers are reluctant to reduce captal durng perods of captal growth by ncreasng the dvdend payout rate. 3. Hypotheses: Captal Structure and Leverage In ths secton, we dscuss economc factors that nfluence nsurer decsons about captalzaton and formulate hypotheses about nsurer captal structure based on fnancal theory. In addton to dscussng the ratonale for nsurers to hold captal, we also formulate hypotheses about frm characterstcs lkely to be assocated wth under- and over-captalzaton. 3.1 Fnancal Dstress The costs of fnancal dstress are a common frcton dentfed as nfluencng captal decsons. As nsurers ncrease ther captal relatve to premums or labltes, the probablty of nsolvency declnes, reducng the assocated expected costs of fnancal dstress. However, holdng captal n an nsurance company s costly because of varous frctons and market mperfectons, ncludng agency costs, costs arsng from adverse selecton and moral hazard, regulatory costs, and corporate ncome taxaton (Merton and Perold 1998). Agency costs for an nsurer nclude the costs of unresolved owner-manager and polcyholder-owner conflcts. For example, managers may take actons that are nconsstent wth the maxmzaton of frm value such as falure to nvest n postve net present value projects whose rsk may be a threat to manageral job securty. Insurance markets are characterzed by adverse selecton and moral hazard, whch lead to hgher costs of captal to the extent that they cannot be fully controlled through contract desgn, underwrtng, and the clams 7
settlement process. Fnally, nsurers ncur sgnfcant regulatory costs and costs from corporate ncome taxaton to the extent that these costs cannot be fully passed along to polcyholders n premum rates charged for nsurance (Cummns, Grace, and Phllps 1999, Cummns and Grace 1994). Because of these and other captal costs, nsurers do not hold suffcent captal to reduce the probablty of bankruptcy to neglgble levels. Fnancal dstress occurs when an nsurer has dffculty honorng commtments to polcyholders and other credtors. The assocated costs nclude the transactons costs of bankruptcy, the loss of talented employees, the loss of non-marketable and relatonshp-specfc assets, reputaton losses, and other losses to the nsurer's franchse value. Further, nsurance s prced as rsky debt, and the prces an nsurer's products command n the market are nversely related to the probablty of bankruptcy (Sommer 1996, Cummns and Danzon 1997). All else equal, as the expected costs of nsolvency ncrease, the margnal beneft from holdng equty captal ncreases, and the optmal leverage rato (e.g., premums-to-surplus or labltes-to-surplus) decreases. For an nsurance company, the probablty of nsolvency s related to an nsurer's ablty to dversfy rsk. As proxes for nsolvency rsk, we defne three measures of lablty rsk and one measure of asset rsk. The frst measure of lablty rsk s the nsurer's dversfcaton across geographcal areas. Other thngs beng equal, an nsurer that s more geographcally dversfed s expected to have lower nsolvency rsk than nsurers that are more concentrated geographcally. To measure geographcal dversfcaton, we use a Herfndahl ndex of nsurer premum wrtngs by state. The second measure of lablty rsk s the nsurer's Herfndahl ndex across lnes of nsurance based on premum volume. 3 Insurers that are more dversfed by lne are expected to have lower nsolvency rsk than nsurers concentratng on one or a few busness lnes. Lower Herfndahl ndces mply hgher dversfcaton 3 The Herfndahl ndces are, respectvely, the sum of squares of the percentages of premums wrtten by state and the sum of squares of the percentages of premums wrtten by lne. 8
and, consequently, the geographcal and lne of busness Herfndahl ndces are predcted to be postvely related to the use of captal. The thrd measure of lablty rsk focuses on the nsurer's use of rensurance. Because rensurance represents dversfcaton among nsurance companes, frms that purchase more rensurance are expected to have lower nsolvency rsk. Our measure of the ntensty of an nsurer's rensurance actvtes s the rato of ceded loss reserves to drect plus assumed loss reserves. 4 We predct an nverse relatonshp between the rensurance varable and the utlzaton of captal. The measure of asset rsk used n our analyss s the percentage of an nsurer's assets nvested n stocks and real estate, because these assets expose nsurers to more volatlty rsk than ther fxed ncome nvestments, whch tend to be hghly rated bonds and notes. We expect a postve relatonshp between the percentage of assets n stocks and real estate and the utlzaton of captal. These propostons are stated formally n the followng hypotheses. H1. The Herfndahl ndces of premums wrtten by state and by lne of busness wll be postvely related to captal utlzaton. H2. Frms wth hgher ratos of ceded loss reserves to drect plus assumed loss reserves wll use less captal. H3. Frms wth hgher percentages of assets nvested n stocks and real estate wll use more captal. Part of the ncrease n captalzaton levels n the nsurance ndustry may be attrbutable to changes n the characterstcs of nsured rsks. Buyers have substtuted a varety of ''alternatve rsk transfer'' mechansms for nsurance, removng the more predctable rsks and contnung to nsure the more volatle rsks such as commercal lablty clams. If nsurer lablty portfolos have become ncreasngly volatle, ths could provde an explanaton of recent captalzaton trends. 5 Rsk levels 4 Ceded reserves are the labltes that an nsurer transfers to rensurers. Drect reserves represent the nsurer's oblgatons n the prmary nsurance market, and assumed reserves reflect ts oblgatons to other nsurers as a rensurer. Larger ratos of ceded loss reserves to drect plus assumed reserves ndcate more use of rensurance. 5 Changes n asset portfolo rsk also could help to explan the changng captalzaton levels n the ndustry. However, except for an ncrease n the proporton of assets held n corporate equtes, prmarly due to unrealzed captal gans, n general nsurer asset portfolos have changed lttle over our sample perod. We control for the 9
also are expected to dffer cross-sectonally among frms n the ndustry as a functon of both underwrtng and nvestment portfolo choces. To control dfferences n ncome volatlty across nsurers, we use the standard devaton of each nsurer's book-value ROE computed over the three years precedng each analyss year. We expect ths varable to be postvely related to captalzaton. H4. Hgher rsk, as measured by the standard devaton of ROE, wll be assocated wth hgher captal utlzaton. It s well known from statstcal and actuaral theory that the average loss n a pool of rsks becomes more predctable as the number of rsks n the pool ncreases. Ths means that the losses of larger nsurers are more predctable than those of smaller frms so that large frms should requre relatvely lower captalzaton to acheve a gven level of nsolvency rsk. Although n prncple smaller frms should be able to acheve smlar results through rensurance, n practce rensurance s costly due to frctons such as moral hazard, adverse selecton, and the need to provde a proft to the rensurer. Followng the recent nsurance effcency lterature (Cummns and Wess 2000), we use the natural log of frm assets to represent frm sze and propose the followng hypothess: H5. Captalzaton wll be nversely related to frm sze. 3.2 Agency Costs There are two prmary sources of agency costs n the nsurance ndustry: owner-manager conflcts and owner-polcyholder conflcts. Conflcts between owners and managers arse because managers do not share fully n the resdual clam held by owners and have an ncentve to behave opportunstcally. Conflcts between owners and polcyholders arse because polcyholders' clams to assets have legal prorty over owners' clams. Owners have an ncentve to explot polcyholder nterests by changng the rsk structure of the frm or takng actons that ncrease the value of equty, perhaps by decreasng the value of the polcyholders' debt clam on the frm. The owner-manager conflct s a classc example of moral hazard, snce the non-contractble ncreased mportance of corporate equtes by ncludng the rato of stocks and real estate to total assets as an ndependent varable n our emprcal analyss. 10
effort of the manager drectly affects the value of the clam held by the owner. Wthout possessng a 100 percent ownershp stake, managers face a reduced margnal beneft from nvestng ther effort nto the frm, alterng the ncentves for the manager to exert the optmal effort. Ths creates a sgnfcant agency cost that can be reduced by ncreasng leverage. Holdng constant the managers' level of ownershp, reducng equty captal ncreases the managers' stake n the frm, helpng to algn the nterests of owners and managers. Reducng equty also decreases the amount of free cash avalable for managers to pursue prvate nterests, such as takng on projects that ncrease the sze of the frm but do not maxmze the value of equty. Fnally, addtonal leverage ncreases the probablty of bankruptcy (a partcularly costly event for managers), makng value-destroyng pursuts more costly for managers. Mtgatng the conflct between managers and owners thus consttutes a beneft from ncreased leverage. When owners and polcyholders are separate classes of nvestors, a conflct arses because owners have a clam to frm value only beyond the clams of polcyholders. Due to lmted lablty, equty ownershp s equvalent to a call opton on the value of the frm, makng rsky nvestments attractve to owners. Snce polcyholders bear much of the consequences of faled nvestments, polcyholders prefer less rsky nvestments. When the opportunstc behavor of owners s antcpated, the effect s ncorporated nto the prce of nsurance, and owners bear much of the cost of the ncentve conflct. Ths cost can be reduced by decreasng leverage, whch mtgates the prce effect by reducng nsolvency rsk. Further, ncreasng the amount of equty captal relatve to premums reduces the beneft to owners from substtutng rsker nvestments, makng asset substtuton less attractve. Mtgatng the conflct between polcyholders and owners thus consttutes a beneft from decreased leverage. Jensen and Mecklng (1976) argue that the optmal captal structure s determned by tradng off the benefts from ncreased leverage (mtgatng the owner-manager conflct) wth the benefts 11
from decreased leverage (mtgatng the owner-polcyholder conflct). When the owner-manager conflct s partcularly severe, frms may appear under-captalzed to the extent that agency costs are not fully reflected n the cost of captal used n our effcency analyss. When the owner-polcyholder conflct s severe, frms may appear over-captalzed. Because both stock and mutual nsurers are present n the nsurance ndustry, organzatonal form provdes an excellent proxy for the degree of agency costs nherent n an nsurance frm. Compared wth stock companes, mutuals control the owner-polcyholder conflct by mergng these two roles. However, the owner-manager conflct s more severe n the mutual ownershp form because the mechansms avalable for owners to control managers are much more lmted than n the stock ownershp form. In a ratonal market, one would expect the benefts from removng the ownerpolcyholder conflct to exceed the costs of unresolved owner-manager conflcts n mutual nsurance frms. Consequently, the elmnaton of the owner-polcyholder conflct s lkely to result n a reduced margnal beneft from holdng captal n mutuals, suggestng that mutuals may be less captalzed than stocks, other thngs equal. Mutuals also may have less need for captal than stocks because they tend to nvest n less complex or less rsky projects requrng lmted manageral dscreton n prcng and underwrtng (Lamm-Tennant and Starks 1993). On the other hand, mutuals may have a greater tendency than stocks to hoard captal durng proftable perods because of ther lmted ablty to access captal markets n the event of a shock to captal. In addton, to the extent that holdng addtonal captal provdes benefts to managers (e.g., from controllng larger nvestment portfolos), mutuals may hold captal n excess of optmal levels because of a msalgnment of polcyholder and manager nterests. Because we do not have an unambguous predcton about ownershp form, we state the followng hypothess n null form: H6. Mutuals wll not utlze captal more or less ntensvely than stocks. Due to the tme lag between payment of premums and payment of clams, nsurance frm managers are n control of polcyholder funds for a sgnfcant perod of tme. Ths tme lag offers 12
managers the opportunty for engagng n actvtes that provde prvate benefts, possbly to the detrment of the frm and polcyholders. As the polcy length and clams tal ncreases, the problem worsens; and there s a beneft to removng excess funds from the frm and ncreasng the bankruptcy probablty. Reducng captal and ncreasng leverage can accomplsh ths. An nsurer's loss reserve and unearned premum reserve are labltes for losses not yet pad and premums receved for whch servce has not yet been provded. The rato of the sum of loss and unearned premum reserves to ncurred losses s used as a proxy for tme lag between polcy ssuance and the payment of clams, wth hgher ratos ndcatng longer taled busness. As ths rato ncreases, the margnal cost of captal ncreases and frms are predcted to choose lower captal levels. Thus, we hypothesze that: H7. The rato of reserves to losses ncurred wll be nversely related to captal utlzaton. 3.3 Asymmetrc Informaton and Growth Opportuntes If corporate managers possess superor nformaton about the frm's assets n place and new nvestment opportuntes than do owners, Myers and Majluf (1984) argue that these nformaton asymmetres may cause managers to forego postve net present value projects. Ths results n a ''peckng order'' theory of fnancng where managers prefer fnancng through nternal funds and debt rather than ssung new equty. As the degree of asymmetry between managers and nvestors ncreases, ths under-nvestment problem worsens and rasng equty captal becomes more costly. The mplcatons of the Myers-Majluf theory for our analyss depend upon the degree of the nformatonal asymmetry problem n the nsurance ndustry and the response to the problem by the frms n the ndustry. Because property-lablty nsurers nvest prmarly n marketable securtes, there are mnmal nformatonal asymmetres from the asset sde of the balance sheet, except perhaps wth respect to the credt rsk of recevables from agents and rensurers. The prncpal nformatonal asymmetry for property-lablty nsurers arses from uncertanty about the true value of reserves for the payment of unpad losses, whch averages about 65 percent of total labltes, ndustry-wde. A substantal component of the loss reserve represents nsurer estmates of the clams to be pad n the 13
future on long-tal polces such as commercal lablty nsurance. Insurers have sgnfcant actuaral and accountng flexblty n determnng the stated loss reserve, and most of the nformaton needed to evaluate the accuracy of reserve estmates s not avalable outsde the nsurer. Hence, there are sgnfcant nformaton asymmetres between managers and nvestors wth regard to the labltes for long-taled nsurance polces, especally n the commercal lnes. Insurers may respond to the nformatonal asymmetry problem by buldng up slack captal durng proftable perods to provde nternal funds to nvest n attractve future projects. Alternatvely, nsurers wth relatvely hgh nformaton asymmetres may become more hghly leveraged, especally durng unproftable phases of the underwrtng cycles, because they are at a net dsadvantage n rasng new equty relatve to nsurers whose labltes are more transparent to nvestors. That s, f nsurers wth the greatest reservng uncertanty have equal ablty to generate retaned earnngs as nsurers wth more transparent labltes, the former group wll lkely become more hghly leveraged over tme because ts costs of rasng external captal are hgher. Moreover, frms wth hgher reserve uncertanty may actually be less successful n generatng retaned earnngs because long-tal lnes of nsurance tend to generate less ncome from underwrtng than shorter-tal lnes. Thus, such nsurers may be dsadvantaged n rasng both nternal and external captal, mplyng that nformaton asymmetres between managers and owners are more lkely to lead to hgher leverage rather than addtonal slack captal n the nsurance ndustry. Another mplcaton of the Myers-Majluf theory s that for any gven degree of nformatonal asymmetry, frms wth more growth opportuntes are expected to hold addtonal captal to avod the need for rasng costly captal n the future. Ths dscusson suggests the followng hypotheses: H8. Frms wth hgher nformaton asymmetres between managers and owners wll be more hghly leveraged than frms wth lower nformaton asymmetres. H9. Frms wth more growth opportuntes wll hold relatvely more equty captal. The standard devaton of ROE over tme s used as a proxy for the degree of nformaton asymmetres between managers and nvestors. Insurers wth low earnngs volatlty are assumed to 14
possess assets and labltes that change very lttle over tme, makng ther future proftablty easly conveyed from manager to nvestor. However, nsurers wth hgher volatlty have operatons that are less predctable, and therefore have more severe nformaton asymmetres than less rsky nsurers. Based on ths ratonale, the standard devaton of ROE s predcted to be nversely related to captalzaton. Recall, however, that H4 predcts a postve relatonshp between ROE rsk and captal, based on the fnancal dstress costs argument. Thus, the sgn of ths varable wll depend upon the extent to whch t measures frm opacty versus the probablty of fnancal dstress. The rato of reserves to losses ncurred, dscussed n connecton wth H7, also serves as a proxy for nformatonal asymmetres, to the extent that lengthenng the clams payment tal ncreases uncertanty about reserve accuracy. The reserves varable thus has a predcted negatve sgn under both H7 and H9. To proxy for growth opportuntes, we use the one-year percentage growth rate n premums. As the measure of growth ncreases, t s hypotheszed that nsurers wll be motvated to hold more captal to be able to take advantage of growth opportuntes usng nternal rather than external funds. Thus, the premum growth rate s predcted to be postvely related to captal utlzaton. 3.4 Product Market Interacton Because the purpose of nsurance s to dversfy rsk and ndemnfy polcyholders for losses due to contngent events, the nsurance market s senstve to nsurer nsolvency rsk, and safer nsurers command hgher prces. In addton, postve swtchng costs and prvate nformaton possessed by the ncumbent nsurer can create a sgnfcant advantage to remanng wth the same nsurer (Kunreuther and Pauly 1986, D'Arcy and Doherty 1990). Due to economes of scale and the exstence of nsurance brokers, corporate nsurance buyers face sgnfcantly lower swtchng costs than personal buyers, makng relatonshps wth corporate buyers more fragle than those wth personal buyers. The commercal lnes nsurance market s consdered a ''commodty market,'' where buyers choose nsurers on the bass of prce, from the set of nsurers wth adequate (often A or better) 15
fnancal ratngs (.e., the market s characterzed by a tendency for ''flght to qualty''). Moreover, commercal lnes buyers and ther brokers are more profcent than ndvdual buyers n assessng nsurer fnancal qualty, suggestng the followng hypothess: H10. Captalzaton wll be nversely related to the percentage of an nsurer's revenues comng from personal lnes of nsurance. To test H10, we nclude n the regressons the rato of the nsurer's personal lnes premums to total premums. Ths varable s expected to be nversely related to captalzaton. We predct a negatve coeffcent on the personal lnes varable based on the flght to qualty argument. 3.5 Regulaton In response to an ncrease n nsurer nsolvences n the 1980s and early 1990s, the Natonal Assocaton of Insurance Commssoners (NAIC) nsttuted rsk-based captal (RBC) requrements n 1994. Varous regulatory actons are stpulated f the rato of the nsurer's actual captal to rsk-based captal falls below a seres of thresholds begnnng at 200 percent (see Cummns, Grace, and Phllps 1999). The ntroducton of rsk-based captal created a regulatory opton that reduced the market value of nsurers. Because the opton value s nversely related to captalzaton, the ntroducton of RBC s predcted to have ncreased captalzaton levels n the ndustry. To control for dfferences n captalzaton by year, we nclude year dummy varables n our regresson equatons. If captal levels were adjusted followng the RBC ntroducton year (1994), the coeffcents of the year dummy varables may be larger n the later years of the sample perod. On the other hand, f nsurers antcpated the ntroducton of RBC, any captal adjustments may have occurred pror to our sample perod, and the year dummy varable coeffcents wll have no systematc pattern. 4. Hypotheses: Revenue Effcency and Return on Equty In addton to regressons to explan nsurer captal structure, we also conduct regressons desgned to detect relatonshps between captal structure and frm performance. We use two ndcators of performance - revenue effcency and book-value return on equty (ROE). In ths secton, we dscuss hypotheses and expected sgns for the frm performance regressons. 16
4.1 Revenue Effcency The prmary purpose of the revenue effcency analyss s to determne whether measured captal under- or over-utlzaton s a ratonal strategy that s rewarded by the market wth addtonal revenues or a true neffcency that leads to revenue penaltes. The mantaned hypothess about the relatonshp between captalzaton and revenue effcency s that nsurance buyers are senstve to nsolvency rsk but that nsurance market equlbrum occurs at a non-neglgble probablty of default. The prmary reason s that holdng equty captal n an nsurance company s costly because of the varous market, tax, and regulatory frctons dscussed above. Thus, at some pont, the margnal beneft of addng captal to reduce nsolvency rsk falls below the margnal cost of the added captal, producng an optmal captal-to-assets rato that maxmzes frm value. Our analyss of cost effcency enables us to estmate the optmal quantty of captal for each frm n the sample. Frms wll be rewarded or penalzed for measured sub-optmal captal utlzaton dependng upon whether holdng captal that devates from the measured optmum represents a legtmate response to market forces or a true neffcency. Sub-optmal captal-utlzaton does not represent a true neffcency f captal levels reflect legtmate dfferences n captal requrements across frms because of heterogenety n underwrtng or nvestment portfolos, corporate governance, or other factors. On the other hand, f devatons from optmal captal represent a true neffcency, nsurers holdng sub-optmal amounts of captal are lkely to be penalzed by the market n terms of lower revenues. Ths s ether because they hold too lttle captal and thus have hgher nsolvency rsk than buyers fnd desrable or because they hold too much captal and perhaps try to recover the costs of the excess captal by chargng prces that buyers vew as too hgh. To test the relatonshp between revenue effcency and captal utlzaton, we use as an explanatory varable the sub-optmal captal-to-assets rato, defned as the rato of actual mnus optmal captal-to-assets. If measured captal under- or over-utlzaton represents legtmate usage of captal, the sub-optmal captal-to-assets rato s expected to be postvely related to revenue 17
effcency. However, f measured under- or over-utlzaton reflects neffcency, the sub-optmal captal-to-assets rato s expected to be negatvely related to revenue effcency. In order to determne whether the market responds symmetrcally to captal under and over-utlzaton, we defne two addtonal varables based on the sub-optmal captal-to-assets rato the captal over-utlzaton rato, whch s equal to the sub-optmal captal-to-assets rato when that varable s postve and equal to zero otherwse, and the captal under-utlzaton rato, whch s equal to the sub-optmal captal-toassets rato when that varable s negatve and zero otherwse. Most of the explanatory varables dscussed n the precedng secton also are ncluded n the revenue effcency regressons, prmarly as control varables. In most cases, the expected sgns of the explanatory varables are ambguous a pror. For example, the lne of busness Herfndahl ndex s predcted to have a negatve sgn under the conglomeraton hypothess, whch holds that t s valuemaxmzng for frms to offer multple lnes of busness, ether because of dversfcaton benefts or because buyers are wllng to pay more for ''one-stop shoppng.'' On the other hand, the strategc focus hypothess, whch holds that frms can maxmze value through focusng on one or a few lnes of busness where the frm has a comparatve advantage, predcts that the lne of busness dversfcaton varable wll have a postve sgn, recallng that hgh Herfndahl ndces mply more concentraton. 6 Lkewse, the geographcal Herfndahl ndex could have a postve or negatve sgn dependng upon whether focusng on a narrower geographcal area allows the frm to become more knowledgeable about the market and hence to buld stronger relatonshps wth customers versus reducng rsk through dversfcaton. Gven that there are other varables n the equaton relatng more drectly to nsolvency rsk, a postve sgn on the geographcal Herfndahl may be more lkely than a negatve sgn. Interpretng asset rsk as ndcatve of hgher nsolvency probabltes, we expect the rato of stocks and real estate to assets to be nversely related to revenue effcency. Frm sze s expected to be postvely related to revenue effcency f larger frms have lower 6 The conglomeraton and strategc focus hypotheses are further dscussed further n Berger, et al. (2000). 18
nsolvency rsk and/or are able to earn hgher revenues because sze conveys market power. The mutual dummy varable s predcted to have a negatve coeffcent f mutuals are less effcent than stocks due to unresolved agency conflcts that allow managers to behave neffcently. The premum growth rate s expected to have a postve sgn f frms wth more growth opportuntes tend to generate hgher revenues, other thngs equal. Fnally, the proporton of personal lnes output to total nsurance output s predcted to have a negatve sgn f commercal lnes nsurers have lower nsolvency rsk or hgher value-added because of hgher servce ntensty n the commercal lnes. 4.2 Return on Equty The ROE regressons are desgned to provde addtonal nformaton on the relatonshp between frm performance and captalzaton. Agan, we seek to determne whether measured captal under- or over-utlzaton s a ratonal response to market forces or a true neffcency. Fnancal theory predcts that frms wth relatvely more equty (lower leverage) are less rsky and thus should have lower costs of equty captal. Consequently, to the extent that realzed returns on equty are correlated wth the ex-ante cost of captal, we expect the rato of optmal captal-toassets to have a negatve coeffcent n the ROE regressons. If holdng addtonal captal above or below the measured optmum s a ratonal strategy, the rato of sub-optmal captal-to-assets s also expected to have a negatve coeffcent of roughly the same magntude as the coeffcent of the optmal captal-to-assets varable. However, f holdng too much or too lttle captal represents neffcency, the leverage-reducng benefts of holdng addtonal captal wll be partally or fully offset by a market penalty for the neffcency. Hence, the sub-optmal captal-to-assets rato could be negatve wth a smaller (n absolute value) coeffcent than the optmal captal-to-assets rato or concevably could be nsgnfcant or postvely related to ROE. Also ncluded n an ROE regresson s the frm's revenue effcency score and an ndcator varable set equal to 1 f an nsurer has a Best's ratng of A or hgher and equal to zero otherwse. To 19
the extent that hghly rated frms can charge hgher premums because of buyer perceptons that they have lower nsolvency rsk, we predct a postve coeffcent for the Best's ratng ndcator varable. The revenue effcency score s also predcted to be postvely related to ROE because revenue effcent frms lose smaller proportons of ther revenues due to neffcency, gvng them hgher profts, other thngs equal. The Best's ratng varable and revenue effcency are jontly determned wth ROE. Consequently, they are treated as endogenous varables, usng an nstrumental varables approach dscussed below. The explanatory varables ncluded n the revenue effcency regressons also are ncluded n the ROE regressons. There are several unambguous predctons based on the fnancal theory relatonshp between rsk and return. If geographcal and lne of busness dversfcaton reduce frm rsk, the coeffcents on the geographcal and lne of busness Herfndahl ndces are predcted to be postve n the ROE regressons because hgher Herfndahl ndces mply less dversfcaton and a hgher cost of captal. The rato of stocks and real estate to total assets also has a predcted postve coeffcent due to the hypotheszed relatonshp between rsk and the cost of captal. Lkewse, f buyng more rensurance reduces frm rsk, our rensurance varable, the rato of ceded loss reserves to drect plus assumed loss reserves, s predcted to be nversely related to ROE. Frms wth more growth opportuntes are lkely to be vewed favorably by captal markets, predctng a negatve sgn on the premum growth varable. Based on our argument that commercal lnes nsurers wll be relatvely safe compared to personal lnes nsurers, we predct a postve coeffcent on the rato of personal lnes output to total nsurance output. The predcted sgn of the sze varable n the ROE regresson s ambguous. On the one hand, f larger frms are more dversfed than smaller frms, we would expect sze to be nversely related to ROE. On the other hand, f larger frms earn hgher revenues due to market power, sze could be postvely related to ROE. In ths regard, t would reflect the frm's earnng economc rents rather than a hgher ex ante cost of captal. The predcted sgn of the long tal lnes varable (loss reserves 20
dvded by losses ncurred) s also ambguous. If long-tal lnes are more rsky than short-tal lnes and/or frms wth more long-tal busness are more hghly levered, a postve coeffcent would be predcted. On the other hand, long-tal lnes are known to have lower underwrtng profts than shorttal lnes because long-tal premums have a hgher dscount for the tme value of money. If ths effect domnates, the long-tal lnes varable could have a negatve coeffcent n the ROE regressons. Fnally, f mutual frms are more hghly levered than stocks, the mutual dummy varable s predcted to have a postve coeffcent, but f mutual frms wrte lower rsk busness than stock frms (Lamm-Tennant and Starks 1993), the mutual varable could have a negatve coeffcent. 5. METHODOLOGY Ths secton dscusses the estmaton methodologes used n our analyss of frm captal structure and performance. We begn by dscussng the economc effcency concepts underlyng our analyss. Next, we dscuss the estmaton of effcency utlzng (DEA). The secton concludes wth a dscusson of the regresson methodology used to analyze captal structure and the sub-optmal captal utlzaton on frm performance. 5.1 Effcency To analyze producton fronters, we utlze nput-orented dstance functons (Farrell 1957, x = x, x,..., 2 x K ' R + Shephard 1970). Suppose producers use nput vector ( ) K M vector y = ( y, y,..., 1 2 )' R +. The dstance functon ( y x) y M 1 to produce output D, s nterpreted ntutvely as the dstance of a gven frm's output-nput vector ( y, x) from the best practce producton fronter. For a sngle-nput, sngle-output frm, the fronter can be envsoned as an upward slopng lne n ( x, y) space. The operatng ponts of fully effcent frms, D ( y, x) = 1, le on the fronter, ndcatng that they operate wth the mnmum amount of nputs needed to produce ther quantty of output. Ineffcent frms, D ( y, x) > 1, le to the rght of the fronter, ndcatng that they could reduce ther nput consumpton whle producng the same quantty of output f they operated on the fronter (.e., 21
were fully effcent). More formally, we can defne the dstance functon n terms of the producton technology that transforms the K nputs nto M outputs. The producton technology s represented by the nput correspondence ( y)= V { x ( y, x) frm as D( y, x) sup{ θ : x V ( y) }. ( y x) = θ : s feasble}. The nput-orented dstance functon for a specfc D, s equal to 1 for effcent frms because they are already on the fronter and hence cannot reduce ther nput usage. ( y, x) > 1 D for neffcent frms and equals the recprocal of the mnmum equ-proportonal contracton of the nput vector x that can stll produce y. A smlar nterpretaton can be gven to the dstance functons wth respect to the cost and revenue fronters dscussed below. 7 The Farrell measure of nput techncal effcency reflects the ablty of a frm to mnmze nputs utlzed to produce a gven quantty of output. It s defned as TE 1, = = nf{ θ : θx V ( y) }. D ( y x) ( y, x) The techncal effcency measure θ s equvalent to one mnus the equ-proportonal reducton n all nputs that stll allows producton of the same outputs. It follows that TE ( y, x) 1. The Farrell measure of techncal effcency can be estmated wth respect to a producton fronter characterzed by constant returns to scale (CRS) or varable returns to scale (VRS). From an economc perspectve, frms should operate wth CRS, so total techncal effcency s gven by Farrell effcency wth respect to a CRS fronter, ( y x) respect to a VRS fronter, PTE( y x) TEVRS ( y, x) TE CRS,. Pure techncal effcency s gven by Farrell effcency wth, =, and scale effcency s gven by the remanng total techncal neffcency not explaned by pure techncal effcency, SE( y x) where SE ( y, x) denotes scale effcency. Frms wth ( y, x) = 1 SE are operatng wth CRS. ( y, x) ( y, x) TECRS, =, TE VRS 7 For further dscusson of dstance functons and operatng fronters see Charnes, et al. (1994), Grosskopf (1993) and Lovell (1993). 22
By explctly modelng the economc objectve of cost mnmzaton, we can estmate the cost effcency of each frm. When the economc objectve s to mnmze the costs assocated wth producng a gven output, then economc cost effcency s measured by the rato of mnmum possble cost to actual observed cost. Supposng producers face nput prces K ( w1, w2,..., ), the mnmum cost fronter s defned as c( y, x) = mn{ w' x : D( y, x) 1} w = w K ' R + + The optmal nput vector x * mnmzes the costs of producng y gven the nput prces w. Cost effcency then s smply defned as: CE w' x *, =. w' x ( y x) Cost effcency captures pure techncal effcency, scale effcency, and allocatve effcency. Allocatve effcency measures a frm's ablty to mnmze costs usng nputs n the optmal proportons, gven ther relatve prces. Gven a measure of total techncal effcency and cost effcency, allocatve effcency s determned resdually as AE ( y x) ( y, x) ( y, x) CE, =. TE Therefore, we have the followng decomposton of cost effcency: ( y, x) AE( y, x) PTE( y, x) SE( y x) CE =,. Fnally, by specfyng the addtonal economc objectve of maxmzng revenues, we can estmate the revenue effcency of each frm. Assumng output prces ( ) M x p = p, p2,..., p M ' R + + 1, the objectve s revenue maxmzaton, subject to the constrants mposed by nput supples and the producton technology. The revenue maxmzaton problem s: r( y, x) = max{ p' y : D( y, x) 1} Gven the optmal outputs y *, revenue effcency s gven by the rato of actual revenue to p' y RE =. p' y * maxmum revenue: ( y, x) y.. 23
5.2 Data Envelopment Analyss Data envelopment analyss (DEA) s a non-parametrc mathematcal programmng approach to estmatng dstance functons (Charnes, et al. 1994). Assumng the avalablty of nput, output, and prce data for each of N frms, DEA can be used to construct a fronter such that all observed ponts le on or below the fronter. For the th frm, let vectors x, y, and w represent the K, M, and K length column vectors of nputs, outputs, and nput prces. Defne the matrces X, Y, and W as the K N, M N, and K N matrces of nputs, outputs, and nput prces for all frms, = 1,..., N. To measure techncal effcency wth a CRS producton fronter, the followng lnear program s solved for each frm: mn θ subject to: θ λ y θ x Yλ λ 0 Xλ where λ s an N 1 vector for frm representng the combnaton of frms that form the producton * fronter for frm. The soluton θ s a scalar representng the equ-proportonal reducton n nputs for frm that would enable t to produce output vector y f t operated on the producton fronter. A value of θ * = 1 would mply that the frm s operatng on the fronter,.e., no reducton n nputs s possble for frm. Ths program s solved for each frm n the sample, resultng n a techncal effcency score for each frm TE = θ, = 1,..., N. Constranng the λ only to be non-negatve * results n a CRS fronter. The above program s modfed to account for VRS by addng the convexty constrant ι ' N λ = 1, where ι ' N s an N-element vector of 1s. Solvng the lnear programmng problem wth ths constrant yelds a convex hull that envelops the data more tghtly, resultng n an estmate of pure ** techncal effcency (PTE). Denotng the soluton to the modfed program by θ, the estmate of 24
pure techncal effcency s gven by PTE = = θ. Scale effcency s gven by the rato of TE VRS ** * θ the two solutons, SE =. Only f SE = 1 ** has the frm has acheved CRS. θ To estmate cost effcency, the objectve functon of the program s altered to capture total frm costs. The lnear program s specfed as mn w x x λ ' subject to: y x Yλ Xλ λ 0 Lettng * x be the cost mnmzng vector of nputs for frm, cost effcency s gven by CE * w x =. Gven estmates of cost and techncal effcency, allocatve effcency s estmated by w x ' ' the rato CE AE = TE. The soluton of the cost effcency program provdes the cost-mnmzng xk nput vector condtonal on the observed technology n the sample. If the rato < 1, the frm s * x xk under-utlzng nput k; and f > 1, the frm s over-utlzng nput k. * x k Revenue effcency s computed wth a smlar lnear program, where the objectve s changed from cost mnmzaton to revenue maxmzaton k max p y λ ' y subject to: y Y l x X l l 0 Lettng * y be the cost-mnmzng vector of nputs for frm, revenue effcency s gven by 25
p y RE =. p y ' ' * 5.3 Ex-Post Regresson Analyss After estmatng effcency scores and optmal nputs, we estmate regresson models wth the rato of actual-to-optmal captal, revenue effcency, and ROE as dependent varables. Ordnary least squares (OLS) s used to estmate the revenue effcency equaton and a verson of the revenue effcency and ROE regressons. We also estmate a verson of the actual-to-optmal captal regresson that ncludes an ndcator varable set equal to 1 f the frms has an A ratng or better from the A.M. Best Company, and to zero otherwse. Ths s based on the hypothess that a frm's fnancal ratng may help to explan ts captal utlzaton, e.g., frms may add captal n order to be assured of retanng the requste A ratng from Best's. Because the ratng varable s jontly determned wth the frms actual-to-optmal captal rato, OLS estmaton of the verson of the model that ncludes the Best's varable would yeld nconsstent parameter estmates. To correct for ths endogenety problem, the equaton whch ncludes the Best's ndcator varable s estmated usng two alternatve methodologes -- the nverse Mll's (IM) rato approach and an nstrumental varables (IV) approach. The estmaton technques are dscussed n more detal n an Appendx avalable from the authors. In the ROE equaton, we nclude both the Best's ndcator varable and the frm's revenue effcency score as addtonal explanatory varables. The ncluson of the Best's varable s based on the hypothess that frms wth A ratngs or above are lkely to earn economc rents because of the percepton among buyers that such frms have relatvely low nsolvency rsk. The revenue effcency varable s ncluded based on the ratonale that revenue effcent frms are lkely to have hgher returns, because they waste less of ther potental revenues due to neffcency than do neffcent frms. Both varables are expected to be jontly determned wth the dependent varable and thus are treated as endogenous. Because we have both a dchotomous and a contnuous endogenous varable n ths equaton, we control for endogenety usng the IV approach, agan usng the ftted value from 26
a probt model as the nstrument for the dchotomous Best's ratng varable. Revenue effcency s treated as n standard two-stage least squares estmaton. 6. THE SAMPLE, OUTPUTS, AND INPUTS Ths secton dscusses the sample of nsurers analyzed n ths study. We also defne the outputs, nputs, and output and nput prces that we use n estmatng effcency. 6.1 The Sample The prmary source of data for the study conssts of regulatory annual statements fled by nsurers wth the Natonal Assocaton of Insurance Commssoners (NAIC) over the perod 1993 to 1998. The operatng unts n the nsurance ndustry consst of groups of afflated nsurers under common ownershp and unafflated sngle nsurers. The sample conssts of all groups and unafflated nsurers for whch meanngful data were avalable. The number of frms declned from 970 n 1993 to 770 n 1998, prmarly due to consoldaton n the nsurance ndustry. The frms n the sample account for about 94 percent of net wrtten premums n the ndustry. 6.2 Output Quanttes and Prces Consstent wth the recent fnancal nsttutons lterature, the value-added approach s used to defne property-lablty nsurer outputs (Berger and Humphrey 1992). The value-added approach counts as mportant outputs those wth sgnfcant value added, as judged usng operatng cost allocatons. Consstent wth the recent lterature on nsurance effcency (see Cummns and Wess 2000), the prncpal outputs we consder are rsk poolng/rsk bearng, real servces, and fnancal ntermedaton, brefly defned as follows: Rsk-poolng and rsk-bearng. Insurance provdes a mechansm through whch consumers and busnesses exposed to losses can engage n rsk dversfcaton through poolng. For consumers, nsurance dversfcaton provdes value by reducng the uncertanty n ther fnal level of wealth. For busness frms, nsurance adds value by reducng ncome volatlty; thereby reducng expected tax payments, expected costs of fnancal dstress, and the costs of external fnance. The actuaral, underwrtng, and related expenses ncurred n rsk poolng are mportant components of value added n the ndustry. Insurers also add value by holdng equty captal to bear the resdual rsk of the pool. Real fnancal servces relatng to nsured losses. Insurers provde a varety of real servces for polcyholders, ncludng the desgn of rsk management programs and the provson of legal 27
defense n lablty dsputes. By contractng wth nsurers to provde these servces, polcyholders can take advantage of nsurers' expertse to reduce the costs of managng rsk. Fnancal ntermedaton. For property-lablty nsurers, ntermedaton s an mportant but somewhat ncdental functon, resultng from the collecton of premums n advance of clam payments to mnmze contract enforcement costs. Insurers' value added from ntermedaton s reflected n the net nterest margn between the rate of return earned on nvested assets and the rate credted to polcyholders. Transactons flow data such as the number of applcatons processed, the number of polces ssued, the number of clams settled, etc. are not publcly avalable for nsurers. However, a satsfactory proxy for the quantty of rsk-poolng and real nsurance servces output s the present value of real losses ncurred (Berger, Cummns, and Wess 1997, Cummns, Wess, and Z 1999, Cummns and Wess 2000). Losses ncurred are defned as the losses that are expected to be pad as the result of provdng nsurance coverage durng a partcular perod of tme. Because the objectve of rsk-poolng s to collect funds from the polcyholder pool and redstrbute them to those who ncur losses, proxyng output by the amount of losses ncurred seems qute approprate. Losses are also a good proxy for the amount of real servces provded, snce the amount of clams settlement and rsk management servces also are hghly correlated wth loss aggregates. Because the types of servces provded dffer between the prncpal types of nsurance and the tmng of the loss cash flows also vares, we use as separate output measures the present values of personal lnes short-tal losses, personal lnes long-tal losses, commercal lnes short-tal losses, and commercal lnes long-tal losses, where the tal length refers to the length of the loss cash flow stream. 8 Cash flow patterns are estmated from data n Schedule P of the NAIC nsurance regulatory statement usng the Taylor separaton method (see Cummns 1990), and dscountng s conducted usng U.S. Treasury yeld curves obtaned from the Federal Reserve Economc Database (FRED) mantaned by the Federal Reserve Bank of St. Lous. Average real nvested assets for each year are used to measure the quantty of the 8 The lnes of busness are classfed as short and long-tal on the bass of ther classfcaton n Schedule P of the Natonal Assocaton of Insurance Commssoners (NAIC) regulatory annual statement. 28
ntermedaton output. Monetary-valued varables are deflated to real 1989 values usng the consumer prce ndex (CPI). In keepng wth the value-added approach to output measurement, the prces of the nsurance outputs are defned as: p P PV ( L ) ( L ) =, where PV p s the prce of nsurance output, = 1,..., 4 for personal short-tal output, personal long-tal output, commercal short-tal output, and commercal long-tal output. The present value of losses s used n computng the prce because premums reflect mplct dscountng of the loss cash flow stream. Usng present values of losses mantans consstency by recognzng the tme value of money both n the premum and loss components of the prce. 9 Multplyng the prce p by the quantty of output, PV ( ) L, gves the value-added from the th nsurance output. For the prce of the ntermedaton output, we need a measure of the expected rate of return on the nsurer's assets. Although nsurers are prmarly fxed ncome nvestors, equtes represent a sgnfcant proporton of nvested assets for property-lablty nsurers. Accordngly, the expected return on assets should ncorporate the expected returns on both the debt and equty components of nsurer nvestment portfolos. Because the expected return on bonds and notes generally wll be close to the actual return, we use the rato of actual nvestment ncome (mnus dvdends on stocks) to nsurer holdngs of debt nstruments to represent the rate of return on that component of the portfolo. For stocks, we compute the expected return for a specfed year as the 90-day Treasury bll rate at the end of the precedng year plus the long-term (1926 to the end of the precedng year) average market rsk premum on large company stocks from Ibbotson Assocates (1999). Usng ths approach assumes that nsurers have equty portfolos wth a market beta coeffcent of 1.0. 9 Ths s a generalzaton of the nsurance unt prce concept that has been used extensvely n the nsurance economcs lterature (e.g., Pauly, Kunreuther, and Klendorfer 1986). The conventonal unt prce measures the cost of delverng $1 of benefts as the rato of premums to ncurred losses. 29
The expected portfolo rate of return for each nsurer s determned as a weghted average of the debt and equty returns wth weghts equal to the proporton of the total portfolo nvested n debt securtes and stocks. Thus, the prce of the ntermedaton output dffers across nsurers because of varaton both n the return on debt nstruments and n the debt/equty portfolo proportons. 6.3 Input Quanttes and Prces Insurance nputs are classfed nto three groups: labor, materals and busness servces, and fnancal captal. Because nsurers do not report the number of employees or hours worked, the quantty of labor s mputed by dvdng the total expendture on labor by the prce of labor. Denotng the quantty of labor by as c w L, the quantty of labor s defned as Q L, the current dollar expendtures as c L c L c X L, and the current dollar wage rate X Q L =. The real prce of labor s found by deflatng the w current dollar wage rate, w L = w c c L, where c s the consumer prce ndex (CPI). Multplyng the quantty of labor by the real prce of labor thus yelds constant dollar labor expendtures. Current dollar expendtures for labor equal the sum of expendtures for admnstratve labor and agent labor. Admnstratve labor expendtures are obtaned from nsurers' annual statements as the sum of salares, payroll taxes, and employee relatons and welfare expendtures. For agent labor, current dollar expendtures are obtaned from the annual statements as the sum of net commssons and brokerage fees plus allowances to agents. The prce of the labor nput s a weghted average of the prces of admnstratve labor and agent labor, wth weghts equal to expendtures on each category of labor dvded by total labor expendtures. The prce of admnstratve labor s the U.S. Department of Labor average weekly wage rate for property and lablty nsurers (SIC 6331) n the state of the nsurer's home offce. The prce of agent labor s the premum-weghted average of Labor Department's nsurance agents' weekly wage rates (SIC 6411) n states where the nsurer operates, wth weghts equal to the proporton of the nsurer's drect premums wrtten n each state. 30
The quantty of materals and busness servces nputs s also mputed from total expendtures and prces. Current dollar expendtures on materals and busness servces are obtaned from the annual statement as total expenses ncurred less all labor costs. 10 The prce of materals and busness servces nput s gven by a natonal prce ndex for busness servces from the U.S. Department of Commerce. Fnancal captal s ncluded as an nsurer nput snce t s an essental component of the technology that produces the nsurance product. Besdes satsfyng regulatory requrements, equty captal affects the qualty of the nsurance product by reducng the probablty of default. Vewng nsurance as rsky debt, nsurance prces reflect the expected costs assocated wth nsurer default, so captal levels ultmately affect the revenue and proft of an nsurer. Includng captal s especally mportant n the current study, because our objectve s to determne whether nsurers are allocatvely neffcent because of the overuse of equty captal. The quantty of equty captal for an nsurance company s defned as ts statutory polcyholder surplus augmented by reserves requred by statutory (regulatory) accountng but not recognzed by generally accepted accountng prncples (GAAP). 11 The average of begnnng and end-of-year equty captal s used as the nsurer's captal for any gven year. These values are deflated to current dollars usng the CPI. Because the majorty of nsurers are not publcly traded, market equty returns are not observed for most frms n the sample. As an estmate of the cost of equty captal, we adopt an approach utlzed n pror effcency research on property-lablty nsurers (Cummns and Wess 2000). For a gven year, the cost of equty s assumed to be constant for all frms n the ndustry and 10 Ths component of costs captures expendtures on advertsng, board and bureau fees, equpment, prntng, communcatons, audtng, and other busness expenses. Because expendtures on physcal captal such as computers and offce space are a small proporton of total nsurer expenses, physcal captal s ncluded n the materals and busness servces category rather than beng treated separately. 11 The prmary reserves n ths category are the ''provson for rensurance'' and the ''excess of statutory over statement reserves.'' 31
equal to the 90 day Treasury bll rate at the end of the precedng year plus the long-term (1926 to the end of the precedng year) market rsk premum on large frm stocks as reported n Ibbotson Assocates (1999). We recognze that our measure may fal to capture mportant dfferences among frms, makng the ex-post regresson analyss partcularly mportant. Consequently, we nclude varables known to be related to the cost of captal n our regresson analyss. 6.4 Inputs and Outputs: Summary To summarze, we use fve outputs and three nputs. The outputs are the present value of real losses ncurred for personal short-tal, personal long-tal, commercal short-tal, and commercal long-tal coverages as well as total assets, representng the ntermedaton output. The nputs consst of labor, materals and busness servces, and equty captal. 7. RESULTS Ths secton presents the results of our emprcal analyss of nsurer captalzaton. We frst present summary statstcs on the prncpal varables ncluded n our analyss and then turn to a dscusson of the effcency results. The secton concludes by presentng the regresson results for the actual-to-optmal captal rato, revenue effcency, and ROE. 7.1 Summary Statstcs The nputs, nput prces, and expenses of the property-lablty nsurance ndustry for the perod 1993-1998 are shown n Table 2. Input utlzaton and expendtures ncreased over the sample perod for all nputs. However, n percentage terms, the use of labor and materals declned over the sample perod, whereas the percentage of total expenses attrbutable to fnancal captal ncreased (see the lowest panel n Table 2). The fnancal captal percentages are computed n two ways - usng the yearly nput prces and usng the average nput prce for the sample perod. The latter calculaton was conducted n order to solate the effect of the ncrease n the quantty of captal consumed from the change n prce over the perod. When the yearly prces of captal are used, captal ncreased from 20.4 percent of total expenses n 1993 to 32.3 percent n 1998. When the average prce of captal s 32
used, captal ncreased from 23.1 percent of expenses n 1993 to 31.1 percent n 1998. Thus, usage of the captal nput ncreased sgnfcantly n both absolute and relatve terms durng the sample perod. Outputs and revenues are shown n Table 3. The quantty of nsurance output s roughly evenly dvded between the personal and commercal lnes. However, the commercal lnes have hgher prces because these lnes are more rsky and have hgher servce ntensty than personal lnes. Consequently, the majorty of nsurance revenues are attrbutable to the commercal lnes. The ntermedaton output also accounts for a sgnfcant proporton of total revenues. The last secton of the table shows that the percentage of total revenues attrbutable to the ntermedaton functon has ncreased from 33 percent n 1993 to 39 percent n 1998. Addtonal summary statstcs are presented n Table 4, whch shows yearly values and averages of varables used n our regresson models. Notably, the sub-optmal captal-to-asset rato (actual mnus optmal captal over assets) ncreased from 13.3 to 15.4 percent over the sample perod. Otherwse, there are few pronounced trends n the varables, except for an ncrease n the rato of stocks and real estate to total assets from 18.1 percent n 1993 to 21.5 percent n 1998. 7.2 Effcency Results The results of the DEA analyss are presented n Table 5. The average scores, shown for each type of effcency, are comparable to the scores reported n earler research on property-lablty nsurers (Cummns and Wess 1993, Cummns, Wess, and Z 1999). Average cost effcency n the ndustry s about 40.6 percent, based on the sample perod as a whole. Pure techncal neffcency s the prmary source of cost neffcency -- pure techncal effcency averages 57.6 percent, whereas scale and allocatve effcency average 88.8 and 79.8 percent, respectvely. 12 The fndng wth respect to pure techncal neffcency s perhaps not surprsng gven the rapd pace of technologcal change n the past few years. Revenue effcency averages 27.1 percent, ndcatng a hgh degree of revenue 12 Recall that techncal effcency s the product of pure techncal and scale effcency and that cost effcency s the product of techncal and allocatve effcency, although t should be noted that these relatonshps hold at the ndvdual frm level and only as an approxmaton for the averages. 33
neffcency n the ndustry, at least on average. The sources of allocatve neffcency n our sample of nsurers are analyzed n Table 6. Part A of the table shows percentage departures from optmal utlzaton ratos defned as follows: X ( ) U = 100 opt 1, where U s under- or over-utlzaton of nput, X X s actual quantty of nput, and opt X s the optmal quantty of nput. If U > 0, the mplcaton s that nputs are over-utlzed and f U < 0, nputs are under-utlzed. Table 6 reveals that nsurers on average over-utlze all three nputs. The average over-utlzaton of labor s 159.7 percent, ndcatng that neffcent nsurers could reduce labor nput by about 61.5 percent f they operated as effcently as the best practce frms n the ndustry. The over-utlzaton of materals and busness servces s substantally less than for labor, 57.2 percent, mplyng that nsurers could reduce materals nputs by 36.4 percent n total f they were fully effcent.. 13 The over-utlzaton of captal s 85.8 percent on average. The years wth the two largest over-utlzaton estmates are n the second half of the sample perod, provdng some evdence that over-captalzaton has ncreased over tme. On average, nsurers could reduce captal by about 46.2 percent f they were fully effcent. Interestngly, f captal s reduced by 46 percent n 1999, the ndustry's leverage ratos are more algned wth hstorcal averages - 1.6 for the premums-to-surplus rato and 0.20 for the captal-to-assets rato (based on the data underlyng Fgure 1). Ths agan provdes some support for the hypothess that nsurers hoard captal to avod havng to rase external captal followng a loss or nvestment shock. The amount of captal over-utlzaton n bllons of dollars s shown n secton B of the Table 6. Over-utlzaton ncreased by nearly 90 percent over the sample perod, from 66.6 bllon n 1993 to 124.2 bllon n 1998. 7.3 Regresson Analyss The regresson analyss conssts of three equatons wth dependent varables equal to the rato 34
of the nsurer's actual captal to optmal captal, revenue effcency, and ROE, respectvely. The actual-to-optmal captal equaton s desgned to dentfy covarates related to the utlzaton of captal and to test the hypotheses specfed n the theoretcal dscusson presented above. The actual-to-optmal captal regresson equatons are presented n Table 7. Three equatons are shown n the table. The frst equaton, whch s estmated by OLS, omts the Best's ratng ndcator varable because t s jontly determned wth captal. As mentoned above, the Best's ratng varable s set equal to 1 f the frm has an A ratng or better from the A.M. Best Company, and to zero otherwse. The other two equatons nclude the Best's ratng ndcator varable and adjust for ts endogenety usng, respectvely, the nstrumental varables (IV) and the nverse Mll's (IM) methodologes. These methodologes are explaned n an Appendx avalable from the authors. The regressons presented n Table 7 provde support for most of our hypotheses regardng captal utlzaton. The Best's A ratng ndcator varable s postve and sgnfcant n the IV and IM regressons, as expected f frms hold more captal n order to protect ther fnancal ratngs. The rensurance varable has a sgnfcant negatve coeffcent n all three equatons, as expected f use of rensurance s a substtute for holdng captal n terms of reducng the expected costs of fnancal dstress (H2). The rato of stocks and real estate to total assets n postve and sgnfcant n all three equatons, as expected f nsurers hold addtonal captal to compensate for hgher asset portfolo rsk (H3). The natural log of assets s negatve and sgnfcant, provdng support for H5,.e., that rsk s nversely related to the sze of the rsk pool so that larger nsurers need relatvely less equty captal. The mutual dummy varable s negatve and sgnfcant n all three equatons, rejectng H6 and ndcatng that mutuals are less lkely to over-utlze captal than stocks, perhaps because of hgher costs of captal due to unresolved agency conflcts. 14 The rato of nsurance reserves to losses 13 The smaller total percentage reductons ndcate that larger frms are relatvely less neffcent. 14 However, t would not be correct to conclude from these results that mutuals have lower captal-to-assets ratos than stocks. In fact, addtonal regressons (not shown) wth the captal-to-assets rato as the dependent varable ndcate that mutuals have sgnfcantly hgher captal-to-assets ratos than stocks, most lkely to provde a cushon 35
ncurred s negatve and sgnfcant, as predcted f frms wth more long-tal busness are more levered n order to dscourage managers from takng actons that are contrary to the nterests of polcyholders (H7). The standard devaton of book ROE s negatve and sgnfcant n all three equatons. Recall that ths varable s predcted to have a postve coeffcent f t prmarly proxes the probablty of fnancal dstress and a negatve coeffcent f t prmarly captures nformatonal asymmetres between managers and nvestors. The results thus provde evdence consstent wth H8,.e., that frms wth hgher nformatonal asymmetres wll use less equty captal because they face hgher costs of external captal. The sgnfcant negatve coeffcent on the rato of reserves to losses ncurred also s consstent wth H8 to the extent that ths varable captures nformatonal asymmetres n the long-tal lnes of busness. The results wth the standard devaton varable do not provde support for H4,.e., that frms wth hgher standard devatons of ROE wll hold more captal to reduce the expected costs of fnancal dstress. The one-year premum growth rate s postve as expected but s not statstcally sgnfcant. Consequently, the results wth ths varable do not support H9, that frms wth growth opportuntes hold more captal to take advantage of postve net present value projects. The rato of personal nsurance output to total nsurance output s negatve and sgnfcant, consstent wth the argument that commercal buyers are more senstve to nsolvency rsk than personal buyers (H10). Contrary to expectatons, both the geographcal and the lne of busness Herfndahl ndces have negatve sgns n all three equatons shown n Table 7, although only one of the coeffcents s statstcally sgnfcant. Thus, the results do not support H1, that frms that dversfy geographcally and across lnes of busness need less captal. A possble explanaton for these results s that operatng over wder geographcal areas and more lnes of busness exposes nsurers to more rsk for future nvestment and loss shocks because of mutuals lmted ablty to rase new external captal. It s correct to conclude from Table 8 that mutuals are sgnfcantly less lkely to over-utlze captal than stocks. 36
because of the dffcultes n controllng and montorng the underwrtng process n more complex organzatons, possbly offsettng the dversfcaton benefts assocated wth lower Herfndahl ndces. In addton, frms that operate n more states and lnes of busness are lkely to be dealng wth larger and more complex nsurance rsks, necesstatng that they hold more captal. Fnally, Wald tests reveal that there are no sgnfcant dfferences among the ntercept terms for the years 1993, 1994, 1995, 1997, and 1998. The ntercept for 1996 s sgnfcantly dfferent from the ntercepts for the other years, but t s dffcult to attrbute ths result to rsk-based captal, whch went nto effect n 1994. The results thus suggest ether that rsk-based captal had no sgnfcant effects on overall captalzaton n the ndustry or that any captal adjustments predated our sample perod. The revenue effcency and ROE equatons presented n Table 8 are prmarly desgned to provde nformaton on whether measured ''sub-optmal'' captal utlzaton represents a legtmate response to market condtons or a true neffcency that degrades frm performance. The revenue effcency equatons provde evdence consstent wth the vew that sub-optmal captal utlzaton represents a true neffcency. In the frst revenue effcency equaton shown n the table, the sub-optmal captal-to-assets rato has a sgnfcant negatve coeffcent, mplyng that captal over-utlzaton s assocated wth lower revenue effcency. The second revenue effcency equaton breaks out the sub-optmal captal-to-assets rato nto ts postve and negatve components. In ths equaton, the captal over-utlzaton rato has a sgnfcant negatve coeffcent, provdng further evdence that frms over-utlzng captal have lower revenue effcency. However, the captal under-utlzaton rato s not statstcally sgnfcant, suggestng that frms sustan revenue effcency penaltes for captal over-utlzaton but not necessarly for captal under-utlzaton, other thngs equal. Thus, nsurers appear to sustan revenue effcency penaltes for over-utlzng captal, perhaps because ther prces are too hgh, reflectng the deadweght costs of holdng excess captal. The nsgnfcant coeffcent on the captal under-utlzaton rato suggests that frms do not sustan revenue effcency penaltes due to buyers nterpretng captal under-utlzaton as an 37
ndcator of excessve nsolvency rsk, especally consderng the presence n the equaton of other nsolvency rsk proxes such as the optmal captal-to-assets rato and the asset rsk varable. The captal under-utlzaton rato fndng should be nterpreted wth cauton, however, because only 7 percent of the observatons n our sample were measured as under-utlzng captal and the average percentage under-utlzaton s much smaller n absolute value than the percentage over-utlzatons. Nevertheless, the strong result wth the captal over-utlzaton rato supports the hypothess that over-utlzaton represents a true neffcency whch leads to revenue effcency penaltes. The optmal captal-to-assets rato, ncluded as a control varable, has a sgnfcant postve coeffcent, mplyng that frms wth hgher ratos of optmal captal to assets have hgher revenue effcency, other thngs equal. A possble explanaton for ths fndng s that some product market segments may have hgher optmal captal-to-asset ratos and also, perhaps ndependently, relatvely hgh prce competton, leadng to hgher revenue effcency. Such an explanaton would seem to ft the commercal lnes, where buyers are very senstve to nsolvency rsk and prce competton s ntense. The results wth the other explanatory varables n the revenue effcency equaton are mostly consstent wth expectatons. 15 The sze varable s postve and sgnfcant, perhaps suggestng that larger frms have lower nsolvency rsk or that sze conveys advantages n terms of market power. The stock and real estate (asset rsk) varable s negatve and sgnfcant, suggestng that frms wth rsker assets are less revenue effcent. Mutuals are less revenue effcent than stocks, supportng the argument that mutuals have hgher default rsk, and/or suggestng that mutuals are less effcent because of unresolved agency conflcts. The rato of personal nsurance output to total nsurance output and the rato of nsurance reserves to losses ncurred are negatve and sgnfcant, probably 15 The Best's ndcator varable s not ncluded n the revenue effcency regresson because we do not have any reason to hypothesze that a frm's fnancal ratng s a drver of ts revenue effcency. Consequently, ncludng the Best's ratng varable here would not be approprate. When the equaton was re-estmated wth the Best's ndcator varable ncluded, the other varables n the equaton retaned ther sgns and sgnfcance levels. 38
reflectng hgher prces receved n commercal lnes (see Table 3) and hgher complexty n long-tal lnes, whch often results n lower effcency. Contrary to expectatons, both the geographcal and lne of busness Herfndahl ndces are postve and sgnfcant, suggestng that more dversfed frms have lower revenue effcences than less dversfed frms. Ths could suggest that strategc focus s a more successful strategy than conglomeraton n terms of maxmzng revenues. The ROE equatons also are shown n Table 8. The dependent varable n the regressons s ROE before polcyholder dvdends and taxes because ths varable focuses drectly on the frm's market outcome n terms of net ncome, pror to deducton of the dscretonary tems, polcyholder dvdends, and government mandated tax payments. 16 Four versons of the regresson are ncluded n Table 8, two OLS versons that exclude the Best's A ratng ndcator varable and revenue effcency and two nstrumental (IV) varables versons that nclude these potentally endogenous varables. The two OLS and IV versons dffer from one another dependng upon whether the sub-optmal captal to assets rato s ncluded versus ncludng the captal under- and over-utlzaton ratos separately. The ROE regressons provde addtonal evdence that measured sub-optmal captal utlzaton s a true neffcency and that captal over-utlzaton s a more serous problem than captal under-utlzaton. The optmal captal-to-asset rato has a sgnfcant negatve coeffcent n the ROE regressons, consstent wth the fnancal theory predcton that better captalzed frms have lower costs of captal. The sub-optmal captal-to-assets ratos n equatons ROE1 and ROE3 also have sgnfcant negatve coeffcents. However, the coeffcent of ths varable s substantally smaller n absolute value than the coeffcent of the optmal captal-to-assets rato. Ths result s consstent wth the vew that holdng captal n excess of the optmal amount also reduces the frm's cost of captal but by a sgnfcantly smaller margnal amount due to a penalty for neffcency. In the equatons that splt the sub-optmal captal-to-assets rato nto ts postve and negatve components (ROE2 and ROE4), the captal over-utlzaton rato s sgnfcant and negatve wth a 39
sgnfcantly smaller (n absolute value) coeffcent than the optmal captal-to-assets rato, agan supportng the nference that holdng excess captal has a smaller effect on the cost of captal than holdng optmal captal. However, the captal under-utlzaton rato s statstcally nsgnfcant, provdng further support for the argument that captal under-utlzaton does not have a statstcally sgnfcant effect on frm performance, subject to the caveats regardng ths varable dscussed above. The sgns of the other varables n the ROE models are generally consstent wth our theoretcal predctons. The Best's ndcator varable s postve and statstcally sgnfcant n equatons ROE3 and ROE4, provdng evdence that effcent frms wth good fnancal ratngs earn hgher returns. However, revenue effcency s not statstcally related to ROE after controllng for the endogenety of ths varable. Revenue effcency could result n hgher realzed returns or t could be assocated wth a lower ex ante cost of captal. Perhaps these effects offset, leadng to the nsgnfcant result wth ths varable. The geographcal and lne of busness Herfndahl ndces have sgnfcant postve coeffcents, consstent wth the argument that the cost of captal s nversely related to dversfcaton. The rato of stocks and real estate to total assets s postve and sgnfcant, consstent wth the hypotheszed postve relatonshp between rsk and the cost of equty captal. Lkewse, the rensurance varable has a sgnfcant negatve coeffcent, supportng the hypothess that rensurance reduces default rsk. The rato of personal lnes output to total nsurance output has a sgnfcant postve coeffcent, supportng the argument that commercal lnes nsurers have lower default rsk than personal lnes frms. The premum growth rate has a negatve coeffcent n all four equatons, but s not statstcally sgnfcant, provdng only weak evdence that frms wth growth opportuntes have lower costs of captal. The sze varable n the ROE equatons has a sgnfcant postve sgn, consstent wth the argument that larger frms earn hgher profts, other thngs equal, perhaps due to market power. The 16 Robustness checks usng ROE after dvdends but before taxes and ROE after dvdends and taxes support the 40
long tal lnes varable (loss reserves dvded by losses ncurred) s postve and sgnfcant, consstent wth the vew that the cost of captal s hgher for nsurers wrtng long-tal lnes, perhaps because nformaton asymmetres are hgher for these busness lnes. Fnally, the mutual dummy varable s negatve and sgnfcant, provdng some support for the hypothess that mutual frms wrte lower rsk busness than stock frms (Lamm-Tennant and Starks 1993), or perhaps ndcatng that mutuals have lower realzed returns due to unresolved agency conflcts. The overall conclusons to be drawn from the regressons presented n Tables 7 and 8 are the followng: (1) The majorty of the hypotheses about the relatonshps between frm characterstcs and captal utlzaton are supported by the actual-to-optmal captal regressons. (2) Measured captal over-utlzaton prmarly reflects neffcency, for whch nsurers ncur a sgnfcant penalty n terms of revenues. In addton, holdng captal n excess of the optmal amount reduces the cost of captal but by a much smaller margnal amount than holdng optmal captal. Captal under-utlzaton s not sgnfcantly related to ether revenue effcency or ROE n our sample. (3) Frms wth A or better fnancal ratngs earn hgher returns on equty than frms wth lower fnancal ratngs. 8. CONCLUSIONS Ths paper nvestgates the use of equty captal n the property-lablty nsurance ndustry. The nvestgaton s motvated by the sharp declne n ndustry leverage over the past ffteen years. Our objectve s to determne whether the change n relatve captalzaton represents an overutlzaton of captal n the ndustry or a ratonal response to changng market condtons. The prmary source of captal growth n the ndustry over the past ten years s realzed and unrealzed captal gans, whch jontly account for more than 50 percent of the captal ncrease. Pror theoretcal and emprcal evdence suggests that nsurers may tend to ''hoard'' captal durng proftable tmes as a hedge aganst the next underwrtng or nvestment crss. Our analyss of nsurer stockholder dvdend payout rates supports ths argument -- payout rates were actually less n 1995- same conclusons regardng the effects of the optmal and sub-optmal captal to asset ratos on frm performance. 41
1998 than n 1989-1994, even though captal ncreased twce as fast n the latter perod. To further nvestgate the captal over-utlzaton ssue, we estmate techncal, allocatve, cost, and revenue effcency n the ndustry usng a non-parametrc technque, data envelopment analyss (DEA), for the perod 1993-1998. DEA measures the effcency of each frm n our sample relatve to ''best practce'' effcent fronters formed by the fully effcent frms n the ndustry. Fully effcent frms are measured as havng effcency scores of 1, whle neffcent frms have scores between 0 and 1. Cost effcency averages about 40.6 percent, mplyng that nsurers could reduce costs by about 59.4 percent on average f they were to operate wth full effcency. The prmary source of cost neffcency s pure techncal neffcency. Average pure techncal effcency n our sample s 51.2 percent, whereas techncal and allocatve effcency average 89.8 and 79.8 percent, respectvely. These results suggest that falure to adopt state-of-the-art technology s the prmary source of cost neffcency n the ndustry. However, allocatve neffcency s also an mportant a drver of cost neffcency for nsurers. Revenue effcency n the ndustry averages only 27.1 percent durng our sample perod, ndcatve of a sgnfcant loss of potental revenues by the average frm. The results ndcate that frms on average over-utlze all three nputs (labor, captal, and busness servces). Based on a weghted average across the ndustry, nsurers could reduce labor by 61.5 percent, materals by 36.4 percent, and captal by 46.2 percent f they were fully effcent. The results thus provde strong support for the argument that nsurers over-utlze equty captal. When the ratos of premums-to-surplus and captal-to-assets are computed usng optmal ndustry captal rather than actual captal, the ratos are much closer to ther hstorcal averages than to the actual ndustry ratos for 1999. Ths provdes further evdence of captal ''stckness'' n the ndustry,.e., reluctance by nsurers to dstrbute equty captal accumulatons as dvdends. The fnal part of our analyss nvolves estmatng regresson equatons wth three dependent varables - the rato of actual captal to optmal captal, revenue effcency, and ROE. The actual-to- 42
optmal captal regresson supports most of our economc hypotheses regardng nsurer motvatons for holdng captal. We fnd evdence supportng the hypotheses that nsurers hold equty captal to reduce the expected costs of fnancal dstress. We also fnd evdence that rensurance serves as a substtute for equty captal and that nsurer sze s nversely related to the use of equty captal, as expected f larger nsurers are more dversfed. Mutual nsurers are found to have hgher captal-toasset ratos than stock nsurers, but mutuals are less lkely than stocks to over-utlze captal, perhaps reflectng hgher costs of captal. The results also support the hypothess that frms wth greater nformaton asymmetres between managers and nvestors face hgher costs of captal and therefore are more hghly leveraged than frms wth lower nformatonal asymmetres. We also fnd evdence frms wrtng more commercal lnes nsurance hold more captal than frms emphaszng personal lnes, consstent wth greater senstvty to nsolvency rsk among commercal nsurance buyers. There are two opposng nterpretatons that can be gven to the measured sub-optmal captal utlzaton n the ndustry: (1) Because frms hold captal n response to hypotheszed organzatonal and market characterstcs, measured under- or over-utlzaton represents a ratonal response to market condtons that s assocated wth better fnancal performance; or (2) the measured suboptmal captal utlzaton s a true neffcency that degrades the frm performance. The revenue effcency and ROE regressons are used to dstngush between these two possbltes. The results support the second nterpretaton of measured sub-optmal captal utlzaton. Revenue effcency s nversely related to the sub-optmal captal-to-assets rato (the rato of actual captal mnus optmal captal to assets), mplyng that measured sub-optmal captal utlzaton prmarly reflects neffcency. When the sub-optmal captal-to-assets rato s separated nto postve and negatve components, we fnd that revenue effcency has a sgnfcant nverse relatonshp wth captal over-utlzaton but that the captal under-utlzaton varable s not statstcally sgnfcant. Ths suggests that the revenue effcency penaltes prmarly result from usng too much captal rather than too lttle. 43
Return on equty s nversely related to the optmal captal-to-assets rato, consstent wth the argument that better captalzed frms have lower costs of equty captal. The sub-optmal captal-toassets rato also has a negatve coeffcent, but t s much smaller n absolute value than the coeffcent of the optmal captal-to-asset rato, suggestng that the leverage-reducng benefts of holdng above-optmal captal are at least partally offset by a penalty for neffcency. As n the case of revenue effcency, the captal over-utlzaton varable s sgnfcantly related to ROE, but the captal under-utlzaton rato s not statstcally sgnfcant. Overall, we conclude that the run-up n equty captal of the past decade s prmarly attrbutable to captal gans on nvestments. Further, we provde evdence that captal levels n the ndustry are ''stcky'' n the sense that nsurers are reluctant to pay out captal accumulatons as dvdends, preferrng to mantan nternal funds to cushon the captal shocks. Fnally, we fnd that nsurers are over-utlzng equty captal and that the over-utlzaton prmarly represents neffcency that leads to revenue penaltes for neffcent nsurers. 44
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3.0 Fgure 1 Leverage Ratos: 1970-1999 The source of the data s Best's Aggregate and Averages: Property-Casualty Edton (Oldwck, NJ: A.M. Best Co., varous years). The horzontal axs measures calendar years. The left vertcal axs measures the rato of net premums wrtten to equty captal. The rght vertcal axs measures the rato of equty captal to assets. 40.0% 2.5 Premums/Equty Captal 2.0 1.5 1.0 25.0% Equty Captal/Assets 0.5 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 10.0% NPW/Equty Captal Equty Captal/Assets Charts
25% Fgure 2 Growth Rates of Premums and Equty Captal: 6 Year Movng Averages The source of the data s Best's Aggregate and Averages: Property-Casualty Edton (Oldwck, NJ: A.M. Best Co., varous years). The horzontal axs measures calendar years. The vertcal axs measures the 6 year movng average of percentage growth. 20% Percentage Growth 15% 10% 5% 0% 76 78 80 82 84 86 88 90 92 94 96 98 Net Premums Wrtten Equty Captal
TABLE 1 Sources of Equty Captal Growth The source of the data s Best's Aggregates and Averages: Property-Casualty Edton (Oldwck, NJ: A.M. Best Co., varous years). All values are n bllons of U.S. dollars. Total change n surplus s ndustry-wde change n polcyholder surplus durng the calendar year. Percent Pad as Dvdends s the rato of Stockholder Dvdends to the Total Change n Surplus. In Secton B and Secton C, Total Funds s the sum of Retaned Earnngs (non-cg), Realzed Captal Gans, Unrealzed Captal Gans, and Captal Pad-In. Total Change n Surplus Retaned Earnngs (non-cg) Realzed Captal Gans Secton A Unrealzed Captal Captal Gans Pad-In Msc. Surplus Changes Percent Pad as Dvdends 1989 16.04 7.57 4.65 8.03 2.39-5.52-1.08 24.4% 1990 3.49 7.95 2.88-5.12 3.43-5.66 0.00 61.9% 1991 20.12 9.37 4.81 13.43 2.00-5.76-3.73 19.5% 1992 4.21-4.05 9.89-0.06 5.51-6.49-0.59 57.5% 1993 19.25 9.50 9.82 1.05 7.43-7.26-1.29 26.1% 1994 8.12 9.21 1.66-1.81 6.82-6.29-1.47 39.6% 1995 37.54 14.60 6.00 21.72 7.11-8.23-3.65 16.7% 1996 30.60 15.16 9.24 13.31 4.50-8.96-2.64 21.2% 1997 52.87 26.01 10.81 28.98 3.91-11.31-5.53 16.2% 1998 23.51 12.75 18.02 10.24 5.19-13.31-9.38 28.8% 1989-1998 215.74 108.07 77.78 89.76 48.30-78.80-29.37 24.3% 1989-1994 71.22 39.54 33.71 15.51 27.59-36.98-8.16 31.8% 1995-1998 144.52 68.53 44.07 74.24 20.71-41.82-21.21 20.1% Secton B - Percent by Source - Realzed Captal Gans Unrealzed Captal Gans Stockholder Dvdends Stockholder Dvdends Secton C - Percent by Use - Total Funds Retaned Earnngs Captal Pad-In Msc. Uses Retaned Captal 1989-1998 323.90 33.4% 24.0% 27.7% 14.9% 24.3% 9.1% 66.6% 1989-1994 116.36 34.0% 29.0% 13.3% 23.7% 31.8% 7.0% 61.2% 1995-1998 207.55 33.0% 21.2% 35.8% 10.0% 20.1% 10.2% 69.6% Total captal gans (realzed plus unrealzed) are 42.3% for the 1989-1994 perod and 57.0% for the 1995-1998 perod. Assumng equal varances across the tme perods, the estmated standard devaton of the dfference n weghted averages s 0.4% so the dfference s statstcally sgnfcant at better than the 1% level. The 11.6% decrease n stockholder dvdends between the 1989-1994 and 1995-1998 tme perods also s statstcally dfferent from 0 at better than the 1% level. Assumng equal varances across the tme perods, the estmated standard devaton of the dfference n weghted averages s 0.6%.
TABLE 2 Inputs and Expenses Table 2 provdes summary statstcs for the nput quanttes and prces used n the data envelopment analyss. Quanttes and prces are unweghted sample means. The average column reports averages across years. Expenses are the product of nput quanttes and prces. The Percent of Total Expenses reports the rato of expense by nput to total expenses. The fnancal captal percentages are computed n two ways - usng the yearly nput prces and usng the average nput prce for the sample perod. The latter calculaton was conducted n order to solate the effect of the ncrease n the quantty of captal consumed from the change n prce over the perod. 1993 1994 1995 1996 1997 1998 Average Input Quanttes (000s) Admnstratve Labor 3,542 3,614 3,589 3,675 4,116 4,468 3,834 Agent Labor 4,586 4,740 4,818 4,810 5,321 5,952 5,038 Materals & Bus Servces 9,462 9,821 9,606 9,281 9,766 11,383 9,886 Fnancal Captal 146,475 159,684 170,738 191,860 247,040 301,936 202,956 Input Prces Admnstratve Labor 5.087 5.184 5.330 5.485 5.633 5.753 5.412 Agent Labor 4.373 4.401 4.455 4.551 4.677 4.637 4.516 Materals & Bus Servces 2.907 2.874 2.979 3.110 3.271 3.221 3.060 Fnancal Captal 11.5% 12.3% 14.4% 14.1% 14.4% 14.2% 13.5% Expenses (000s) Admnstratve Labor 18,015 18,732 19,131 20,158 23,184 25,708 20,749 Agent Labor 20,055 20,863 21,468 21,890 24,886 27,597 22,750 Materals & Bus Servces 27,501 28,229 28,615 28,866 31,945 36,663 30,256 Fnancal Captal 16,815 19,673 24,518 27,033 35,599 42,905 27,355 Percent of Total Expenses Admnstratve Labor 21.9% 21.4% 20.4% 20.6% 20.1% 19.3% 20.5% Agent Labor 24.3% 23.8% 22.9% 22.3% 21.5% 20.8% 22.5% Materals & Bus Servces 33.4% 32.3% 30.5% 29.5% 27.6% 27.6% 29.9% Fnancal Captal 20.4% 22.5% 26.2% 27.6% 30.8% 32.3% 27.1% Fn Captal: Avg Prce 23.1% 24.1% 25.0% 26.7% 29.4% 31.1% 27.1%
TABLE 3 Outputs and Revenues Table 3 provdes summary statstcs for the nput quanttes and prces used n the data envelopment analyss. Quanttes and prces are unweghted sample means. The average column reports averages across years. Revenues are the product of output quanttes and prces. For the Intermedaton output, revenues are calculated n two ways: frst by usng the yearly prces and second by usng the average prce across years. The Revenues: Percentage of Insurance Output reports the rato of revenues by output to total revenues. The Revenues: Intermedaton as Percentages of Total Output reports the rato of Intermedaton revenues to total revenues usng the two methods of computng Intermedaton revenues. 1993 1994 1995 1996 1997 1998 Average Output Quanttes (000s) Personal Short-Tal 14,699 16,218 17,628 20,186 21,667 24,958 19,226 Personal Long-Tal 43,701 45,001 44,523 47,020 47,491 54,852 47,098 Commercal Short-Tal 27,136 31,921 15,010 15,633 18,244 20,736 21,447 Commercal Long-Tal 40,486 36,332 47,310 45,755 45,521 50,769 44,362 Intermedaton 415,508 438,402 450,330 483,926 569,515 653,153 501,806 Output Prces Personal Short-Tal 0.370 0.323 0.259 0.198 0.245 0.246 0.274 Personal Long-Tal 0.251 0.236 0.308 0.240 0.334 0.337 0.284 Commercal Short-Tal 0.863 0.850 0.986 0.874 0.989 0.887 0.908 Commercal Long-Tal 0.450 0.524 0.642 0.685 0.727 0.690 0.620 Intermedaton 7.0% 6.8% 7.5% 7.4% 7.7% 7.7% 7.3% Revenues (000s) Personal Short-Tal 5,442 5,241 4,574 4,005 5,300 6,133 5,260 Personal Long-Tal 10,987 10,627 13,726 11,282 15,866 18,477 13,397 Commercal Short-Tal 23,412 27,139 14,804 13,670 18,041 18,395 19,480 Commercal Long-Tal 18,213 19,046 30,374 31,358 33,115 35,012 27,494 Intermedaton 28,976 29,909 33,805 35,880 43,918 50,027 36,873 Intermedaton: Avg Prce 30,531 32,214 33,090 35,559 41,848 47,993 36,873 Revenues: Percentages of Insurance Output Personal Short-Tal 9.4% 8.4% 7.2% 6.6% 7.3% 7.9% 8.0% Personal Long-Tal 18.9% 17.1% 21.6% 18.7% 21.9% 23.7% 20.4% Commercal Short-Tal 40.3% 43.7% 23.3% 22.7% 24.9% 23.6% 29.7% Commercal Long-Tal 31.4% 30.7% 47.8% 52.0% 45.8% 44.9% 41.9% Revenues: Intermedaton as Percentages of Total Output Intermedaton 33.3% 32.5% 34.7% 37.3% 37.8% 39.1% 36.0% Intermedaton: Avg Prce 35.1% 35.0% 34.0% 37.0% 36.0% 37.5% 36.0%
TABLE 4 Summary Statstcs: Regresson Varables Table 4 provdes summary statstcs for the varables nput quanttes and prces used n the data envelopment analyss. All reported values are unweghted sample means, except for number of observatons, whch s a sum. Sub-Optmal Captal-to-Assets s the rato of the frms' actual less optmal captal to assets. Captal Over-Utlzaton / Assets s the postve porton of Sub-Optmal Captal-to-Assets, and Captal Under-Utlzaton / Assets s the negatve porton. Optmal Captal-to-Assets s the rato of optmal captal to assets. 1993 1994 1995 1996 1997 1998 Total Sub-Optmal Captal-to-Assets 0.137 0.136 0.135 0.147 0.144 0.155 0.142 Captal Over-Utlzaton / Assets 0.139 0.139 0.138 0.148 0.147 0.156 0.144 Captal Under-Utlzaton / Assets -0.002-0.003-0.003-0.001-0.003-0.001-0.002 Optmal Captal-to-Assets 0.133 0.134 0.133 0.119 0.136 0.131 0.131 Geographcal Herfndahl Index 0.561 0.563 0.573 0.562 0.603 0.589 0.575 Lne of Busness Herfndahl Index 0.448 0.456 0.455 0.462 0.486 0.484 0.465 (Ceded / Gross) Loss Reserves 0.325 0.319 0.322 0.326 0.307 0.309 0.318 (Stock + Real Estate) / Invested Assets 0.184 0.174 0.182 0.189 0.202 0.218 0.191 Natural Log of Assets 18.279 18.299 18.309 18.394 18.195 18.304 18.296 Mutual Dummy Varable 0.451 0.435 0.452 0.448 0.477 0.484 0.458 Insurance Reserves / Losses Incurred 1.388 1.357 1.402 1.363 1.405 1.404 1.387 One-Year Change n Premums 0.135 0.148 0.100 0.108 0.131 0.114 0.123 Personal Lnes Output / Total Output 0.396 0.388 0.401 0.412 0.379 0.379 0.392 Best "A" Ratng Indcator 0.664 0.636 0.649 0.642 0.589 0.602 0.630 Number of Observatons 643 657 646 634 660 628 3,868
TABLE 5 Data Envelopment Analyss Effcency Results Table 5 provdes summary statstcs for the effcency scores for DEA analyss. Sample means and standard devatons are reported by year. The DMU count s the number of decson-makng unts utlzed n the analyss. DMU Pure Total Year Count Techncal Scale Techncal Allocatve Cost Revenue 1993 971 Mean: 0.550 0.934 0.510 0.775 0.393 0.263 Std Dev: 0.228 0.105 0.216 0.152 0.180 0.187 1994 956 Mean: 0.596 0.905 0.535 0.795 0.422 0.271 Std Dev: 0.225 0.127 0.211 0.138 0.175 0.188 1995 949 Mean: 0.569 0.879 0.493 0.844 0.416 0.393 Std Dev: 0.235 0.145 0.216 0.126 0.183 0.333 1996 920 Mean: 0.578 0.907 0.519 0.824 0.425 0.234 Std Dev: 0.229 0.125 0.209 0.154 0.184 0.185 1997 826 Mean: 0.587 0.800 0.486 0.747 0.365 0.202 Std Dev: 0.235 0.220 0.223 0.170 0.200 0.169 1998 770 Mean: 0.581 0.889 0.529 0.799 0.419 0.246 Std Dev: 0.241 0.136 0.217 0.212 0.196 0.187 Total 5,392 Mean: 0.576 0.888 0.512 0.798 0.406 0.271 Std Dev: 0.232 0.152 0.216 0.162 0.187 0.226
TABLE 6 Data Envelopment Analyss Effcency Results Table 6 provdes addtonal summary statstcs from the DEA analyss. Part A of the table shows X U 100 1, percentage departures from optmal utlzaton ratos defned as follows: = ( opt ) where U s under- or over-utlzaton of nput, X s actual quantty of nput, and X s the optmal quantty of nput. If U > 0, the mplcaton s that nputs are over-utlzed and f U < 0, nputs are under-utlzed. Part B shows actual captal, optmal captal, and excess captal, whch s actual less optmal captal. A. Input Over/Under-Utlzaton Total Materals Fnancal Year Labor Servces Captal 1993 204.5% 40.9% 88.1% 1994 183.6% 38.6% 74.0% 1995 145.9% 71.0% 68.7% 1996 123.3% 47.0% 97.9% 1997 207.3% 97.7% 71.5% 1998 123.0% 67.2% 114.7% Total 159.7% 57.2% 85.8% X opt B. Fnancal Captal Utlzaton Actual Optmal Excess Year Captal Captal Captal 1993 142.2 75.6 66.6 1994 152.6 87.7 64.9 1995 161.9 96.0 65.9 1996 176.5 89.2 87.3 1997 204.3 119.1 85.2 1998 232.5 108.3 124.2 Average 178.3 96.0 82.4
TABLE 7 Regresson Models: Captal Utlzaton The endogenous varable s the rato of actual-to-optmal captal. Standard Errors are presented below the estmated coeffcents. *** denotes sgnfcance at the 1 percent level, ** denotes sgnfcance at the 5 percent level, and * denotes sgnfcance at the 10 percent level. Sgnfcance s based on a two-sded test wth a t-dstrbuton. Expected Sgn Ordnary Least Squares Instrumental Varables Inverse Mlls Rato Geographcal Herfndahl Index + -0.045-0.042-0.046 0.058 0.058 0.057 Lne of Busness Herfndahl Index + -0.137 * -0.090-0.094 0.073 0.077 0.077 (Ceded / Gross) Loss Reserves - -0.242 *** -0.193 ** -0.228 *** 0.083 0.087 0.087 (Stock + Real Estate) / Invested Assets + 1.607 *** 1.587 *** 1.570 *** 0.111 0.111 0.111 Natural Log of Assets - -0.160 *** -0.186 *** -0.183 *** 0.011 0.019 0.019 Mutual Dummy Varable Ambguous -0.084 ** -0.110 *** -0.103 *** 0.037 0.039 0.039 Insurance Reserves / Losses Incurred - -0.129 *** -0.128 *** -0.128 *** 0.020 0.020 0.020 Standard Devaton of ROE Ambguous -4.076 *** -3.660 *** -3.842 *** 0.296 0.384 0.383 One-Year Percentage Change n Premums + 0.025 0.027 0.026 0.021 0.021 0.021 Personal Lnes Output / Total Output - -1.883 *** -1.863 *** -1.867 *** 0.059 0.060 0.059 Best "A" Ratng Indcator + 0.259 * 0.840 *** 0.154 0.152 1993 Intercept 6.388 *** 6.633 *** 6.122 *** 0.225 0.266 0.424 1994 Intercept 6.398 *** 6.651 *** 6.140 *** 0.225 0.270 0.428 1995 Intercept 6.393 *** 6.644 *** 6.134 *** 0.225 0.269 0.427 1996 Intercept 6.551 *** 6.807 *** 6.294 *** 0.226 0.271 0.430 1997 Intercept 6.270 *** 6.534 *** 6.015 *** 0.226 0.274 0.434 1998 Intercept 6.356 *** 6.623 *** 6.105 *** 0.227 0.275 0.435 Number of Observatons 3,868 3,868 3,868 Adjusted R-Squared (centered) 0.359 0.369 0.372
TABLE 8 Regresson Models: Revenue Effcency and Return on Equty The endogenous varable s ether revenue effcency or ROE. Standard Errors are presented below the estmated coeffcents. *** denotes sgnfcance at the 1 percent level, ** denotes sgnfcance at the 5 percent level, and * denotes sgnfcance at the 10 percent level. Sgnfcance s based on a two-sded test wth a t-dstrbuton. Revenue Effcency OLS Revenue Effcency OLS ROE ROE ROE ROE OLS OLS IV IV (ROE1) (ROE2) (ROE3) (ROE4) Sub-Optmal Captal-to-Assets -0.264 *** -0.083 *** -0.125 *** 0.024 0.022 0.031 Captal Over-Utlzaton / Assets -0.264 *** -0.089 *** -0.126 *** 0.025 0.023 0.030 Captal Under-Utlzaton / Assets -0.278 0.141-0.108 0.219 0.197 0.223 Optmal Captal-to-Assets 0.137 ** 0.136 ** -0.542 *** -0.523 *** -0.579 *** -0.578 *** 0.061 0.064 0.055 0.058 0.057 0.062 Geographcal Herfndahl Index 0.039 *** 0.039 *** 0.027 *** 0.027 *** 0.027 *** 0.027 *** 0.007 0.007 0.007 0.007 0.007 0.007 Lne of Busness Herfndahl Index 0.072 *** 0.072 *** 0.074 *** 0.074 *** 0.079 *** 0.079 *** 0.009 0.009 0.008 0.008 0.009 0.009 (Ceded / Gross) Loss Reserves -0.021 ** -0.021 ** -0.068 *** -0.068 *** -0.061 *** -0.061 *** 0.011 0.011 0.010 0.010 0.010 0.010 (Stock + Real Estate) / Invested Assets -0.059 *** -0.059 *** 0.066 *** 0.066 *** 0.074 *** 0.074 *** 0.015 0.015 0.014 0.014 0.014 0.014 Natural Log of Assets 0.026 *** 0.026 *** 0.015 *** 0.015 *** 0.008 *** 0.008 *** 0.001 0.002 0.001 0.001 0.003 0.003 Mutual Dummy Varable -0.013 *** -0.013 *** -0.013 *** -0.013 *** -0.017 *** -0.017 *** 0.005 0.005 0.004 0.004 0.004 0.004 Insurance Reserves / Losses Incurred -0.004 * -0.004 * 0.005 * 0.005 * 0.004 * 0.004 * 0.003 0.003 0.002 0.002 0.002 0.002 One-Year Change n Premums 0.003 0.003-0.004-0.004-0.003-0.003 0.003 0.003 0.002 0.002 0.002 0.002 Personal Lnes Output / Total Output -0.092 *** -0.092 *** 0.021 *** 0.020 ** 0.024 *** 0.024 *** 0.009 0.009 0.008 0.008 0.009 0.009 Best "A" Ratng Indcator 0.042 ** 0.042 ** 0.018 0.018 Revenue Effcency 0.033 0.033 0.041 0.041 1993 Intercept -0.174 *** -0.174 *** -0.114 *** -0.114 *** -0.032-0.032 0.034 0.034 0.030 0.030 0.046 0.046 1994 Intercept -0.142 *** -0.142 *** -0.163 *** -0.162 *** -0.080 * -0.080 * 0.034 0.034 0.030 0.030 0.046 0.046 1995 Intercept -0.148 *** -0.148 *** -0.088 *** -0.087 *** -0.005-0.005 0.034 0.034 0.030 0.030 0.046 0.046 1996 Intercept -0.178 *** -0.178 *** -0.139 *** -0.138 *** -0.055-0.055 0.034 0.034 0.030 0.030 0.047 0.047 1997 Intercept -0.186 *** -0.186 *** -0.085 *** -0.084 *** 0.001 0.001 0.034 0.034 0.031 0.031 0.048 0.048 1998 Intercept -0.158 *** -0.158 *** -0.136 *** -0.135 *** -0.051-0.051 0.034 0.034 0.031 0.031 0.047 0.048 Number of Observatons 3,868 3,868 3,868 3,868 3,868 3,868 Adjusted R-Squared (centered) 0.239 0.239 0.186 0.186 0.210 0.210