Temporal Specificity and Task Alignment: Evidence from Patient Care

Transcription

1 Paper to be presented at the DRUID 2011 on INNOVATION, STRATEGY, and STRUCTURE - Organzatons, Insttutons, Systems and Regons at Copenhagen Busness School, Denmark, June 15-17, 2011 Temporal Specfcty and Task Algnment: Evdence from Patent Care Evan Rawley The Wharton School, Unversty of Pennsylvana Management rawley@wharton.upenn.edu Abstract We show how ntegraton solves temporal specfcty problems that arse from the msalgnment of tasks between organzatons and test the predctons of the model, usng a large and rch patent-level dataset on hosptal dscharges to nursng homes and home health care. As predcted by the theory, we fnd that vertcal ntegraton allows hosptals to shft patent recovery tasks downstream to lower cost delvery systems by dschargng patents earler and n poorer health; and ntegraton leads to greater post-hosptalzaton servce ntensty. Whle ntegraton facltates a shft n the allocaton of tasks, health outcomes are no worse when patents receve care from an ntegrated provder. The evdence suggests that by mprovng the algnment of tasks to assets, ntegraton solves temporal specfcty problems that arse n market exchange. Jelcodes:A10,-

2 Temporal Specfcty and Task Algnment: Evdence from Patent Care 1

3 Abstract We show how ntegraton solves temporal specfcty problems that arse from the msalgnment of tasks between organzatons and test the predctons of the model, usng a large and rch patent-level dataset on hosptal dscharges to nursng homes and home health care. As predcted by the theory, we fnd that vertcal ntegraton allows hosptals to shft patent recovery tasks downstream to lower cost delvery systems by dschargng patents earler and n poorer health; and ntegraton leads to greater post-hosptalzaton servce ntensty. Whle ntegraton facltates a shft n the allocaton of tasks, health outcomes are no worse when patents receve care from an ntegrated provder. The evdence suggests that by mprovng the algnment of tasks to assets, ntegraton solves temporal specfcty problems that arse n market exchange. 1. Introducton Ths paper examnes how ntegraton solves temporal specfcty problems that arse from the msalgnment of tasks between organzatons. Temporal specfcty refers to the value lost when an open market transacton s not performed n a tmely manner, compared to the value of the same transacton when performed wthn an ntegrated frm (Masten, Meehan and Snyder 1991). Pror research on temporal specfcty focused on the potental for counterparty opportunsm to create dsruptons n the supply chan by shftng the tmng of exchange away from the technologcally optmal pont. For example, Nckerson and Slverman (2003) demonstrate how the dsrupton of closely coordnated breakbulk operatons n the less-than-truckload (LTL) segment of the truckng ndustry can lead to costly rpple effects throughout the LTL network. As a result, n the presence of temporal specfcty, frms are more lkely to vertcally ntegrate to nternalze the externalty assocated wth the tmng of exchange. We buld on the temporal specfcty lterature by examnng how the tmng of exchange nfluences transacton costs, and extend the lterature by hghlghtng how task algnment, as opposed to ex post opportunsm, nfluences frm boundares. We formalze the ntuton behnd the dea that task msalgnment can be a determnant of temporal specfcty, and test the predctons of the model n the context of the patent care contnuum, where patents transton from acute care facltes (hosptals) nto post-acute care (nursng homes and home health). The emprcal applcaton demonstrates the role of task algnment n transactons and frm boundary decsons. Takng the sequence of clncal nterventons (or tasks) along the care contnuum as fxed patents need a well defned set of clncal nterventons to address ther health care needs exchange s characterzed solely by the tmng of the transton across settngs. Systematc varaton n cost structures between hosptals and post-acute care 2

4 provders and contractual ncompleteness n ther exchange relatonshps ensures that tasks wll not be effcently assgned unless the hosptal and downstream provders are vertcally ntegrated. 1 However, ntegraton costs are non-trval such that there s substantal heterogenety n governance regmes: about half of all hosptals are vertcally ntegrated nto post-acute care. One maor advantage of our emprcal desgn s that we can track patents across organzatons, whch allows us to pnpont how ntegraton nfluences tasks on both sdes of the exchange relatonshp. The ablty to observe the clncal procedures patents receve n post-acute care at a hgh-level of detal s partcularly mportant to our emprcal assessment of patent health at the tme of dscharge. The evdence shows that, on average, vertcal ntegraton leads to shorter hosptal stays for one out of every two patents who are dscharged to a sklled nursng faclty or home health agency. We also fnd that patents receved hgher ntensty of care from vertcally ntegrated home health provders. The results support the central thess of the paper: ntegraton solves task msalgnment problems. Notably, whle we fnd strkng dfferences n the organzaton of servces across stes, vertcal ntegraton does not lead to a declne n patent health outcomes, suggestng that dfferent allocatons of tasks across assets (or stes) produces smlar (or hgher) levels of care qualty. 2 The contrbutons of ths research are twofold. Frst, we develop a tractable model that extends the conceptual bass for temporal specfcty to nclude the role of task algnment. Second, we demonstrate emprcally how vertcal ntegraton changes the algnment of tasks to assets and, thereby, solves temporal specfcty problems that arse n market exchange. 2. Theory and related lterature In ths secton, we descrbe and then formalze the ntuton for task msalgnment as a bass for temporal specfcty, showng that when contracts are ncomplete (for any reason), and counterpartes proft functons are heterogeneous wth respect to a focal task, market exchange wll fal to generate the optmal allocaton of tasks. 1 We focus on Medcare transtons where partes cannot nfluence the prce of exchange and sde payments are llegal. 2 We use the terms assets and stes nterchangeably throughout ths paper. In health care, as n most servce ndustres, tasks may be performed n multple physcal settngs. These settngs can be thought of as assets, as tradtonally defned n the lterature. However, t s perhaps more natural to refer to the locaton of servce provson as a ste. 3

5 Therefore, even when herarchcal governance creates ncentve and bureaucratc costs, task msalgnment can lead to temporal specfcty. The pror lterature on temporal specfcty locates the source of contractng problems n the tmely producton or delvery of goods or servces, an argument that rests on the dea that producton takes a sequental form n whch a sequence of tasks leads to producton of an output. For example, Prrong (1993) fnds evdence that neffcences assocated wth hagglng over quas-rents that arse due to tme-senstve matchng of shpments to carrers leads to long-term contractng and vertcal ntegraton n the bulk shppng market. In the bulk shppng context, shppng must follow producton and precede sales n a pre-determned sequence, and contractng over the tmng of shpments can lead to neffcences because capacty spols f t s not flled when a shp leaves the harbor. Gven a technologcally determned sequence of producton, and the rsks of opportunstc nterruptons or delays amdst the sequence of tasks, the extant lterature analyzes how the tmng of exchange can be affected by ex post maladaptaton. In ths paper, we acknowledge the fundamental nsght that temporal consderatons nfluence the effcency of exchange n a way that creates asset specfcty, but shft the problem back before the emergence of ex post maladaptaton n exchange by studyng temporal specfcty n terms of task msalgnment. Instead of consderng the tmng of exchange as the choce varable, or threat pont, of nterest n a gven transacton, we endogenze the tmng of exchange by analyzng how the parttonng of the sequence of tasks across organzatons (or stes or assets) nfluences producton effcences. Thus, we propose that temporal specfcty need not always arse from opportunstc behavor, but can also be due to producton neffcences n market-based task algnment. In transacton cost economcs (TCE) and the property rghts theory (PRT) of the frm, frms solve neffcences n market exchange arsng from ncomplete contracts and asset specfcty by replacng market exchange wth herarchcal governance (Wllamson 1985, Grossman and Hart 1986, Hart and Moore 1990). Though task algnment, where tasks are defned as producton actvtes (Jacobdes and Wnter 2005), s rarely explctly dscussed n TCE and PRT, the logc behnd these theores would seem to mply that f market exchange led to task msalgnment, frms could solve the externalty by suppressng market mechansms through ntegraton. 4

6 Buldng on the dea that task msalgnment could nfluence transacton costs and the tmng of transactons, we analyze the allocaton of tasks to assets n the case of a two-way vertcal exchange relatonshp, usng a framework where contracts are nherently ncomplete. As s standard n the lterature, we defne ntegraton as the onng of assets under unfed management (Klen, Crawford and Alchan 1978; Wllamson 2010). Transactons are characterzed by exchanges between assets (or stes), and tasks are producton actvtes used n conuncton wth assets to produce outputs for exchange, where, for tractablty, the sequence of tasks needed to acheve an outcome s technologcally pre-determned. Further, we assume that ntegraton results n ncreased bureaucratc costs, arsng from the management of dfferent lnes of busness, as s common n the theory of the frm lterature. We do not, however, mpose exogenous costs of market exchange. Instead, by dstngushng between two types of tasks general and ste-dedcated tasks we express the cost of market exchange through the msalgnment of tasks to stes. The ntroducton of two types of dstnct tasks s crucal because f all tasks are ste-dedcated f all tasks are performed n conuncton wth a partcular ste tasks and assets are redundant constructs and task msalgnment has no substantve meanng beyond the standard TCE/PRT models. In our framework, however, when some tasks are general, that s, when they are not ste-specfc, then task msalgnment can be the bass for temporal specfcty and ntegraton wll nfluence the effcency of the allocaton of tasks across stes. From these foundatons, we propose a model where the allocaton of tasks to stes shapes frm boundares by nfluencng producton costs. To develop ths result, we dvde tasks nto two groups: tasks dedcated to a partcular ste and tasks that can be performed at multple stes. The frst class of tasks ste-dedcated tasks represent the focal source of herarchcal governance costs, as the management of heterogeneous ste-task pars wthn a sngle frm requres costly manageral oversght (Penrose 1959, Schoar 2002). In our model, stededcated tasks are effcently algned, as these tasks never cross the boundares of ther correspondng stes. Our second class of tasks, general tasks, are of partcular nterest, as they may span stes that s, n an exchange relatonshp between two stes, both stes are technologcally capable of performng the general tasks and, therefore, may be allocated to stes dfferently under ntegraton versus market exchange. Thus, n the presence of ncomplete contracts, vertcal ntegraton represents a tradeoff between ncurrng admnstratve neffcences 5

7 from governng addtonal heterogeneous ste-specfc tasks aganst the producton benefts of algnng general tasks optmally to stes. General tasks are the key drver of temporal specfcty problems n our model, as non-cooperatve equlbra may dstort the allocaton of these tasks to stes under market exchange. Ultmately, we show how the msallocaton of general tasks across stes under market exchange creates temporal specfcty that can be solved through ntegraton. We begn wth the smpler benchmark case where all tasks are ste-dedcated and, hence, assets fully partton the task space. For smplcty, we normalze transacton costs from other potental sources to be zero. Under ths assumpton, when all tasks are ste-dedcated, market-based exchange s always superor to vertcal ntegraton; however, once general tasks are ntroduced, ths result may reverse. The tenson between the bureaucratc costs of ntegraton and the cost of producton neffcences assocated wth market exchange leads to two alternatve second best solutons to the problem of exchange. When contracts are ncomplete and tasks cannot be assgned to maxmze total surplus, market exchange can dstort the effcent allocaton of general tasks because frms wll choose how to allocate general tasks to ther own stes wthout nternalzng the externalty mposed on ther exchange partners. By contrast, ntegraton allows the frm to correct producton neffcences assocated wth market exchange by shftng general tasks ether downstream or upstream. On the other hand, ntegraton dampens ncentves and creates bureaucracy costs that are avoded under market exchange. Thus, whle our theory s consstent wth transacton cost economcs models, whch hghlght the tenson between transacton costs and herarchcal governance costs (Wllamson 1985), we explctly model transacton costs n terms of producton neffcences assocated wth task msalgnment. In the smplest case, there are two assets (or stes): A and A. These assets correspond to two tasks: and, such that, task s dedcated to the asset A, whereas task s dedcated to the asset A. and are a mappng from the mportance of the task to the value of ther correspondng assets, A and A. The sze of tasks s fxed technologcally; therefore, n ths case, the value of the two assets s fxed and trvally dependent on matchng the specalzed assets to ther correspondng tasks, wth A > 0 and A > 0. Note that and do not cross the boundares of ther correspondng assets (stes), and under no ntegraton, do not cross the boundares of ther 6

8 correspondng frms. Assets can contrbute dfferently to producton and therefore can generate dfferent payoffs to the frm that owns them. Each asset, A, generates a payoff π(a), whch s ncreasng n the value of the asset, 2 π ( A) π( A) whle the margnal payoff s decreasng n the value of the asset,.e. > 0, < 0. 2 A A The payoffs to vertcal ntegraton are characterzed by: ( A ) + π ( A ) p π, where p s a fxed penalty that depends on characterstcs of the two tasks and. When ntegratng and s costless (.e. p = 0 ), both transactons across frms and transacton wthn frms produce the frst best effcent soluton. As dscussed above, when there are no transacton costs, all tasks are ste-dedcated, and p > 0, vertcal ntegraton wll not take place n equlbrum. On the other hand, n the presence of general tasks, task msalgnment creates temporal specfctes, and as a result vertcal ntegraton may consttute a superor way to organze transactons. To see ths, we ntroduce a thrd task, k, whch s a general one (.e. can be performed by ether A or A ). We further assume that a certan predetermned level of k s needed for technologcal reasons and can be splt across the two assets, A and A, such that: k k + k =. 3 Market exchange s characterzed by the followng sum of payoffs to frms: π A ) + π ( A ). However, the ( effcent allocaton of general tasks across stes may be dstorted when counterpartes proft functons are heterogeneous wth respect to the focal general task. The mportance of the general task, k, and ts allocaton across stes, k, endogenously determnes the tmng of exchange and the larger k the greater the cost of msallocatng t across stes. Contractual ncompleteness, whch we mpose exogenously, mpars arrangements (e.g. sde payments) that would otherwse lead to an assgnment of k that maxmzes total surplus. For example, n our emprcal applcaton, regulaton explctly rules out the sharng of surplus across frms and leads frms to make decsons that may mpose an externalty on ther exchange partner (Robnson 1996). The task ms- 3 For smplcty we treat the level of k as fxed and dscuss neffcences that arse from ts msallocaton across assets. In a less parsmonous model, the level of k could vary as well, such that market exchange leads to under-performance or overperformance of k. Ths would create an addtonal source of neffcency, arsng from market exchange. 7

9 algnment externalty and, therefore, the temporal specfcty assocated wth market-based exchange ncreases wth the mportance of the general task, k, and s only nternalzed through vertcal ntegraton. Snce frms on both sdes of the exchange cannot share the benefts from maxmzng total surplus, yet together they must perform a certan predetermned level of k n order to produce output, the choce of k and k s modeled as the result of a barganng process. Followng the statc axomatc theory of barganng, we assume that the market allocaton of k results n a Pareto optmal symmetrc Nash barganng soluton (Nash 1953; Bnmore, Rubnsten and Wolnsky 1986). Interestngly, snce k s fxed (.e. there s a fxed level of k that must be carred out for the payoff to be postve), the barganng process nvolves two unque elements: frst, the frms threat ponts equal zero and second, barganng exsts even f the sum of both frms proposals s less than k (.e. frms bargan over k even f k s undesrable). Assume frm owns asset A and frm owns asset A. Denote the ~ ~ frms proposed level of k as k, k ) and the Nash barganng soluton as k, k ). In the smplest case, frms are ( ( symmetrc and, therefore, desre the same level of k. In one extreme, k s equally undesrable (.e.( k, k ) = (0,0) ), whle n the other, k s equally desred by both frms (.e.( k, k ) = ( k, k) ). The Nash barganng soluton, n both these cases, s ~ ~ k k ( k, k ) = (, ). More generally, the soluton to the Nash barganng problem corresponds 2 2 to k ~ ~ ~ that maxmzes the Nash product k k ( k k ) k, n ths case, a product of utltes descrbed as the dstance between the Nash barganng soluton and the desred amounts of k. The general soluton s gven by: ~ ( k + k ) k k = k and 2 ~ ( k + k ) k k = k. 2 It s easy to see that when k = k, the symmetrc Nash barganng soluton ~ ~ k k ( k, k ) = (, ) s acheved. 2 2 Under the model assumptons, there s a sngle effcent combnaton (exchange pont) that maxmzes the ont * * profts across frms, such that π ( A ( k )) + π ( A ( k )) > π ( A ( k )) + π ( A ( k )) for all ( k, k ) k, and, n 8

10 ~ ~ * * ~ ~ partcular when k, k ) = ( k, k ), such that: π ( A ( k )) + π ( A ( k )) > π ( A ( k )) + π ( A ( k )). (See Fgure 1 ( * * for a graphcal llustraton). The par ( k, ), chosen by the ntegrated frm, s not the result of market exchange. k Frms, n our model, wll decde to vertcally ntegrate when: * * (1) π VI = π ( A ( k )) + π ( A ( k )) p > π ( A ( k)) + π ( A ( k )) = π ME Ths decson depends on the composton of,, and k. In partcular, the greater k s and the smaller p s, the more lkely t s that the frms would vertcally ntegrate (see Fgure 2). Note, that snce both market exchange and * * vertcal ntegraton nvolve cost, the frst best payoff π ( A ( k )) + π ( A ( k )) s not attanable. The nteracton between ste-dedcated and general tasks s crucal for the allocaton of general tasks across stes. When ste-dedcated and general tasks are complements (an ncrease n one task rases the margnal value of the other task), frms would beneft from concentratng general tasks n stes to maxmze payoff. Alternatvely, there can be dseconomes of scope n tasks. In the case of economes of scope (or task complementarly). A ( ) ( k A k > 0, k k ) > 0 the allocaton of the general task to a sngle ste wll rase the margnal value of the ste-dedcated tasks performed usng that ste. In ths case, the ntegrated frm would maxmze total surplus by performng the entre general task at the ste that provdes t wth the greatest return. On the other hand, when frms make decsons n solaton and are precluded from sharng any surplus from cooperaton, barganng over k wll lead both frms to neffcently perform non-zero amounts of k. If tasks are technologcally determned to be performed sequentally, ths neffcency s properly defned as a temporal specfcty problem snce the msallocaton of tasks leads to a tmng problem n exchange. Task algnment nfluences the cost of market exchange, n our model, by creatng producton neffcences that are due to temporal specfcty, a problem that exsts when there are economes of scope as well as dseconomes of scope (appendx omtted). Gven contractual ncompleteness and dvergent preferences over the allocaton of general tasks to stes, task msalgnment wll lead to temporal specfcty and ntegraton wll sometmes be superor to market exchange even n the presence of postve bureaucratc costs of ont ownershp, p. Thus, our smple model advances the 9

11 dea that vertcal ntegraton and the allocaton of (general) tasks to stes s ontly determned, whch has a number of testable mplcatons. In partcular, when contracts are ncomplete and performng a general task s costly to both exchange partners, as n our emprcal applcaton, vertcal ntegraton wll lead to a shft n the allocaton of general tasks, such that the low-cost ste performs the bulk (or all) of the undesrable general task. We beleve our model s the frst to explctly consder the role of task algnment and temporal specfcty, but, of course, the model s not completely novel. Indeed, our approach follows n the sprt of Grossman and Hart (1986) and Hart and Moore (1990) n that the owners of the upstream and the downstream assets/stes have the resdual rghts to control all aspects of producton, n partcular, the tmng of exchange, whch cannot be explctly gven away by contract. Whle ther work focuses on vertcal ntegraton as a soluton to ex ante noncontractble nvestments, whch are ex post contractble, we focus on task msalgnment problems that occur even when the state of the world s realzed and there s no ex post opportunsm. In our model, exogenous factors (e.g., regulatory restrctons) preclude effcent rent sharng ex post, whch means effcent outcomes can only be acheved through ntegraton. Corts s (2006) formal analyss of the allocaton of tasks to assets n a stylzed model of the trackng ndustry s also smlar to ours n some mportant respects. In Corts s (2006) model a sngle asset (a truck) and a potentally delegable task (mantenance) are allocated between a prncpal (a frm) and an agent (a drver). When the prncpal delegates the mantenance task downstream, effcency dctates asset ownershp by the agent, whch n turn results n greater effort n performng the delegated task. As n our model, Corts lnks task allocaton and asset ownershp, but n hs model prncpal asset ownershp hnders the delegaton of tasks to the agent. In contrast, our analyss reles on the noton that asset (or ste) ownershp facltates task delegaton to acheve an effcent allocaton of tasks. 3. Emprcal context: From hosptals to post-acute-care settngs In order to focus our predctons, we map the theoretcal constructs developed n secton 2 (above) to our emprcal settng. Broadly speakng, we test the predctons of the model by comparng practce patterns between vertcally ntegrated (.e., hosptals wth home health agences and hosptals wth sklled nursng facltes) and non-ntegrated provders along the contnuum of care from acute to post-acute care settngs. The emprcal 10

12 context s appealng for at least four maor of reasons. Frst, contracts are nherently ncomplete between hosptals and post-acute care provders because they are subect to fxed prces set by Medcare wth strct prohbtons on sde payments between hosptals and post-acute provders. Fxed prce exchanges are partcularly lkely to gve rse to ncomplete contractng because the counterpartes cannot use prce to adust for supply and demand mbalances n blateral exchange. Lmtatons on sde payments make t dffcult for relatonal contracts to remedy the rgdtes of fxed prce exchange. Second, there are clear cut ste-dedcated and general tasks n ths settng, and the tmng of exchange nfluences the effcency of care n a drect and mportant way. Hosptals perform specalzed hosptal-dedcated acute care tasks, such as surgery, but once patents are stablzed, post-operatve care rapdly becomes a task that need not necessarly be bundled wth the physcal nfrastructure of a hosptal (.e. post-operatve care becomes a general task once the patent s stablzed). Home health agences and sklled nursng facltes also delver stededcated and general tasks, provdng care servces that are only performed n patents homes 4 or n the sklled nursng faclty, 5 and assstng patents wth recuperatng n a manner that s customzed to the lvng envronment, but also offerng a range of servces that could be provded n a hosptal settng, partcularly montorng, therapy, and recovery servces. These general tasks are produced at much hgher cost n a hosptal settng compared wth a post-acute settng, whch, when coupled wth ncomplete contracts, creates temporal specfcty and the mpetus for vertcal ntegraton. On the other hand, hosptal ntegraton wth sklled nursng facltes and/or home health provders creates bureaucratc oversght costs for the ntegrated entty. Thrd, the health servces ndustry s a collecton of hundreds of dstnct local markets that produce roughly homogenous outputs. We explot the varaton n local market condtons n our emprcal desgn to overcome the effect of selecton on unobservables to dentfy the mpact of vertcal ntegraton on health outcomes; yet, the homogenous nature of outputs across markets facltates an accurate comparson of the effects of vertcal 4 Home health care s sklled health care servces provded n the home, for a lmted duraton; most often by regstered nurses, rehabltatve therapsts, socal workers, or home health ades. An epsode of home health care s a set of vsts over a lmted number of weeks n whch each vst lasts approxmately 1-2 hours. 5 Sklled nursng facltes (also called long-term care facltes or nursng homes) are establshments that house chroncally ll, often elderly patents, and provde post-acute and long-term nursng care. Importantly, for the purposes of ths study, sklled nursng faclty servces are offered by free-standng and hosptal-based facltes. 11

13 ntegraton on hosptals across markets. Fnally, we have access to a large and novel dataset on hundreds of thousands of patents medcal hstory records that tracks ther care across facltes, allowng us to measure the mpact of vertcal ntegraton on the allocaton of tasks to stes at an unusual level of detal. Medcare remburses care delvered by home health agences and sklled nursng facltes through a Prospectve Payment System (PPS). Under PPS for home care, a fxed rembursement s gven for a 60-day epsode ndependent of the number of vsts durng the epsode. Rembursement s fxed and prospectve as the amount s set at admsson, accordng to the observable severty of the patent's condton, and s not altered based on the ntensty of care delvered. In the case of sklled nursng facltes, rembursement s gven for each day of stay (up to 100 days) ndependent of the ntensty of care whle at the faclty. Each epsode payment s adusted for dfferences n labor costs across geographc areas. Wthn ths rembursement strategy, sklled nursng facltes and home health agences are free to provde the ntensty of care that they deem approprate for ther patent. In general, the amount of servce provded does not change the amount of rembursement, whch strengthens the foundaton for our assumpton that contracts are ncomplete n our emprcal context. Gven that the key assumptons of the model are met n the exchange relatonshps between hosptals and post-acute care provders contracts are ncomplete and general tasks can be performed at ether hosptal or postacute care stes the predctons of the model apply to the emprcal context. In partcular, we examne whether hosptals that are vertcally ntegrated dscharge ther patents to sklled nursng facltes and home health agences sooner and when the patents are n poorer health compared to non-ntegrated hosptals. The two predctons arse drectly from the dea that vertcal ntegraton allows hosptals to allocate general tasks (.e., recovery tasks) to ther own sklled nursng faclty and home health agency n a manner that s more effcent than under market exchange, subect to a bureaucratc cost penalty for ntegratng acute and post-acute organzatons. Takng the ntegraton penalty to be postve, but of a magntude that vares by upstream frmdownstream frm par based on exogenous factors, we can nfer the nature of the benefts of vertcal ntegraton by studyng the behavor of effcency maxmzng hosptals. The model predcts that vertcally ntegrated frms wll solve the temporal specfcty problem by shftng the general task to the low-cost provder sooner, here the sklled nursng faclty or home health agency. Thus, t follows that vertcally ntegrated hosptals, whle 12

14 mantanng the same overall qualty of care, wll allocate recovery tasks to the downstream frm by shftng patents to t sooner n the recovery process and when the patent requres more extensve montorng (.e., when they are n worse health). Therefore, the three predctons of the model that we test n our context are: Hypothess 1: Vertcally ntegrated hosptals wll transton patents to sklled nursng facltes and home health agences faster than non-ntegrated hosptals. Hypothess 2: Vertcally ntegrated hosptals wll transton patents to ther own home health agences when the patents are n need of more ntensve montorng and recovery servces. 6 Hypothess 3: Overall qualty of care need not be lower for patents transtonng faster and n worse health wthn vertcally ntegrated hosptals compared to market-based transtons. Whle our key predctons are formally derved from a general model of task algnment, they are consstent wth an nformal health economcs lterature on vertcal ntegraton n hosptals, whch notes that patents can be expected to be dscharged to post-acute care n poorer health and faster when transtonng to post-acute care wthn an ntegrated hosptal system snce ntegraton elmnates opportunsm (Robnson 1996, Lehrman and Shore 1998). Yet, opportunsm s unlkely to drve temporal specfcty problems n the context of patent care snce hosptals tend to have market power versus post-acute care provders and are not ted to blateral exchange relatonshps wth any partcular post-acute care provder. If a post-acute care provder tred to hold-up the hosptal, the hosptal could dscharge patents to another provder, especally f the problem were systematc. The realty of the stuaton s that hosptals cannot dscharge patents at the optmal tme because care provders wll not accept patents on whom they wll lose money. Therefore, n the patent care settng, neffcences are more 6 Ideally, we would test all three hypotheses developed for patents that transton to ether sklled nursng facltes (SNF) or home health agences. Unfortunately, there s no observable measure of care ntensty (to the econometrcan) n SNFs, so we confne our analyses n the SNF settng to tests of Hypotheses 1 and 3. 13

15 lkely to be due to non-cooperatve equlbra that stem from restrctons on rent sharng. Thus, the temporal specfcty problem s not due to hold-up, but rather to contractual ncompleteness and task msalgnment. 4. Data and samples Havng shown how our model of temporal specfcty and task algnment apples, n the context of patent care, we now turn to the emprcal analyss. Our core data come from the Medcare Provder and Analyss Revew (MEDPAR) Fles for The MEDPAR s a research fle compled by the Center for Medcare and Medcad Servces, based on the bllng clams of faclty stays for fee-for-servce Medcare benefcares. Each MEDPAR record represents a faclty stay ncludng acute-care-hosptal stays and sklled nursng faclty stays. It summarzes servces provded to a benefcary from tme of admsson to a faclty through dscharge. Each record ncludes: date of admsson and dscharge; codes for up to 5 procedures and 10 dagnoses (DRG); socoeconomc nformaton; and a unque dentfcaton number that s specfc to a benefcary and the hosptal. Ths s a nearcomplete record of health care faclty encounters for Amercans over 65. To dentfy and characterze post-acute care home health care epsodes that follow hosptalzatons, we lnk the MEDPAR fle acute-care-hosptal stays to the Medcare clams for sklled nursng facltes and home health servces by the scrambled dentfer of the Medcare benefcary. Home health servces are recorded on the Medcare Home Health Agency Standard Analytcal Fles. We dentfy admssons to sklled nursng facltes and home health care agences as those occurrng wthn 3 days of the hosptal dscharge. Because all qualfyng sklled nursng faclty and home health care epsodes of Medcare benefcares are pad by Medcare, these clams fles are a complete record of home health use for the benefcares wth MEDPAR hosptalzatons. We also capture data on home health care servces provded, ncludng number of home health vsts, the dates and types of vsts as well as unque home health agency dentfers. We augment the clams data wth survey data on hosptal organzaton from the Amercan Hosptal Assocaton (2005) and wth data from regulatory reports: for hosptals from the 2005 Hosptal Cost Reports and for sklled nursng facltes and home health agences from the 2005 Provder of Servce Fles. We use these three sources of data to determne whether hosptals are vertcally ntegrated nto sklled nursng facltes and nto 14

16 home health. We conservatvely code hosptals as beng vertcally ntegrated when all three sources agree, though our results are robust to other crtera. Our analyss focuses on MEDPAR hosptalzatons for new health events that resulted n post-acute care admssons ether drectly nto sklled nursng facltes or nto home health, leavng us wth 399,368 dscharges to home health and 460,597 dscharges to sklled nursng facltes from 2,571 hosptals. See Tables I-A and I-B for summary statstcs for patents, hosptals and markets (countes) for dscharges to home health and sklled nursng facltes, respectvely. Our man explanatory varable s whether a hosptal s vertcally ntegrated nto home health or sklled nursng (VI_HOSP), a bnary varable that s equal to unty f a hosptal owns at least one home health agency and zero otherwse. Our dependent varables ndex the predctons of our hypotheses: dscharges wll be faster n vertcally ntegrated hosptals (H1); patents from ntegrated hosptals wll requre more ntensve montorng and recovery tasks upon admsson to home health (H2); and health outcomes need not be negatvely affected by ntegraton (H3). To measure how quckly a hosptal dscharges ther patents, we use a measure of length of stay n the hosptal (LOS) that s computed relatve to the average length of stay of smlar patents n other hosptals by demeanng from the natonal average length of stay wthn each Dagnoss Related Group. The second dependent varable captures the mpact of ntegraton on the (downstream) ntensty of home health care provson. The ntensty of home health care s measured as the number of vsts to a patent s home dvded by the number of days the patent remans n the care of a home health agency, where vsts are weghted by the average wages by occupaton of the home health provder as determned from the 2004 Current Populaton Survey. Our thrd dependent varable s one of the crucal observable measures of the qualty of care patents receve along the care contnuum and the center of polcy debates: patent rehosptalzaton rate. 5. Emprcal desgn We test the predctons of the model by focusng on how length of stay, home health ntensty, and rehosptalzaton rates (wthn 60 days of a dscharge) vary between patents from non-ntegrated and hosptals that are vertcally ntegrated nto home health care and sklled nursng facltes. Snce general tasks montorng 15

17 and recovery actvtes are costly to perform n our emprcal settng, the model predcts that vertcally ntegrated hosptals wll use fat to force ts downstream facltes to accept patents () faster and () n poorer health compared to n an arm s length exchange, but that vertcally ntegrated hosptals wll manage the cost savngs opportuntes such that () rehosptalzaton rates are no greater than n non-ntegrated settngs. Whle we are concerned wth the endogenety of vertcal ntegraton, 7 we frst test these predctons usng the smple OLS model (2): (2) Y l = a + β 1 VI h + X c β c + e, where l ndexes patents, h ndexes hosptals, and Y measures three outcomes: length of stay n the hosptal (LOS), ntensty of care n home health, and rehosptalzaton rates. VI s an ndcator varable that s equal to unty when the hosptal s vertcally ntegrated nto home health and zero otherwse, X s a vector of patent, hosptal, home health agency and market controls that mght plausbly shft hosptal practce patterns. Patent level controls nclude varables that capture the health of the patent at admsson, measured by 28 comorbdtes as well as patents demographc characterstcs, such as age, gender and race. Hosptal controls nclude a set of dummes for ownershp (for-proft, not-for-proft, and government), teachng status, and the number of lcensed beds. Market controls nclude demographc varables such as the average years of schoolng of the local populaton, medan ncome, the percentage of the populaton over age 65, the percentage of the populaton of chldbearng age (females aged 15-44), populaton densty, and a categorcal varable for metropoltan areas; supply shfters ncludng the total number of hosptal beds, sklled nursng faclty beds, and the number of longterm care beds n the market; and the strength of nsurance companes, measured by HMO enrollment rate. 7 Although we nclude a large number of detaled controls, the cross-sectonal nature of the analyss precludes us from makng strong causal nferences from the OLS results, partcularly n tests of the frst hypothess that vertcal ntegraton leads to shorter length of stay. Snce both vertcal ntegraton and length of stay are choce varable for hosptals, our results are vulnerable to selecton bases that lead to heterogeneous treatment effects and omtted varable bas. Whle t s possble that our OLS estmates could be based downward due to selecton nto vertcal ntegraton based on (hgh) qualty, t seems more plausble that the OLS estmates of vertcal ntegraton on length of stay wll be based toward zero as vertcally ntegrated hosptals tend to be nsttutons wth care management phlosophes that emphasze more extensve care delvery over management of fnancal obectves. For example, non-proft hosptals are sometmes thought to over delver servces, at least compared to a for-proft benchmark. Whle proft status s observable, the hosptal s care management phlosophy s not, and we must therefore be concerned that our OLS estmates wll confound the causal effect of vertcal ntegraton wth selecton effects. 16

18 We deal wth the endogenety of vertcal ntegraton usng two approaches. Frst, we adust for selecton on observable dfferences between patent populatons, by matchng post-acute care patents from ntegrated hosptals to patents from non- ntegrated hosptals, based on all observable characterstcs of patents, hosptals and markets. To do so, we use the Coarsened Exact Matchng (CEM) procedure descrbed by Iacus, Kng and Porro (2009), whch facltates mult-dmensonal exact matchng. CEM s smlar to standard two-stage matchng teccnques n that t controls for selecton bas by elmnatng non-analogous observatons n the treatment (.e. ntegrated) and control (.e., non- ntegrated) populatons, but has some techncal advantages over standard matchng approaches. However, no matchng method can control for sources of heterogenety that arse from unobservable characterstcs of hosptals. To adust for selecton on unobservables, we explot varaton n local market condtons n the health servces ndustry, usng the rate of vertcal ntegraton nto home health or sklled nursng facltes by other hosptals n the same market (weghted by patent volume) as an nstrument for the focal hosptal s decson to vertcally ntegrate nto home health (VI_HOSP -h ). Other hosptals ntegraton decsons should not have any drect effect on a focal hosptal s practce patterns, partcularly gven the extensve patent, hosptal and market controls n specfcaton (1); yet, ntervews wth ndustry leaders and experts suggest that hosptal ntegraton decsons are often determned by dosyncratc local market condtons. Thus, our nstrument satsfes the excluson restrcton and has the potental to be a powerful explanatory varable n the frst stage of a two-stage procedure that adusts for selecton on unobservables. 8 Because our man concern s wth the endogenety of hosptal decsons, our key tests of Hypotheses 1 and 3 apply the nstrument VI_HOSP -h to correct for selecton on unobservables at the hosptal-level. Specfcally, we use the two-stage resdual ncluson (2SRI) method frst proposed by Hausman (1978) and more recently by Terza, Basu and Rathouz (2008). The frst stage of our 2SRI procedure s a logt model predctng hosptal vertcal ntegraton nto home health or sklled nursng facltes (VI_HOSP),ncludng all of the controls n (1) 8 A practcal drawback of our nstrumental varable s that t only generates market-level varaton; we could not dentfy any hosptal-level shfters of the costs or benefts of dversfcaton that would satsfy the excluson restrcton. However, we fnd that our nstrument generates substantal between-hosptal varaton n practce, snce the 2,571 hosptals n our sample operate n hundreds of dfferent local markets. 17

19 aggregated to the hosptal level, where the ntegraton rate of other hosptals n the same market s the source of exogenous varaton n each hosptal s vertcal ntegraton decson. The second stage of the 2SRI procedure ncludes the resdual from the frst stage, whch by defnton s uncorrelated wth the covarates n X n (1), and controls for selecton nto vertcal ntegraton based on unobservables. 2SRI estmators have econometrc propertes that are smlar to other two-stage estmators, lke two-stage least squares (2SLS), but are partcularly well suted for our applcaton; mportantly, they are consstent when endogenous regressors are non-lnear and have correct asymptotc standard errors n the frst stage, whch facltates a two-stage nstrumental varables approach at two dfferent levels of analyss (.e., hosptal and patent) wthout manually adustng the standard errors. As a robustness check, we perform a smlar analyss, usng the more famlar 2SLS estmator, whch predcts vertcal ntegraton wth a frst stage lnear probablty model, replacng the explanatory varable (VI_HOSP) n the second stage wth the predcted probablty of vertcal ntegraton nto home health. We also verfy that our results are robust to matchng usng CEM pror to 2SRI estmaton. Tests of our second hypothess that vertcally ntegrated hosptals wll dscharge patents to ther own (vertcally ntegrated) home health agences when the patents requre more ntensve care compare the outcome resultng from the choce of home health ntensty by vertcally ntegrated hosptals wth the outcome from market exchanges between non-ntegrated hosptals and home health agences, usng OLS on the full and matched samples. 6. Results Table II Panel A shows the relatonshp between hosptals vertcally ntegrated nto home health and average length of stay at the patent-level. Column 1 reports a raw correlaton between vertcally ntegraton and length of stay. Includng the full set of patent, hosptal and market controls reduces the pont estmate to -0.06, and the coeffcent estmate becomes ndstngushable from zero (column 2). However, the results n Column 3 demonstrate that patent-level selecton effects bas the OLS results toward zero as the coeffcent estmate on VI_HOSP n the matched sample ncreases to Columns 4-I and 4-II reveal the strength of our nstrument and the nfluence of omtted varable bas on the OLS estmates. Column 4-I s the frst stage nstrumental varables regresson predctng vertcal ntegraton at the hosptal level. The nstrument VI_HOSP -h other 18

20 hosptals rate of vertcal ntegraton n the same market (weghted by patent volume) s very strong: the F- statstc on VI_HOSP -h n the frst stage s 63, and a 1% ncrease n the market vertcal ntegraton rate leads to a 0.31% ncrease n a focal hosptal s propensty to vertcally ntegrate. The second stage of our nstrumental varables approach ncludes the resdual from the frst stage to adust for the effects of unobservable hosptalspecfc factors that mght nfluence vertcal ntegraton decsons. The, result s a pont estmate on the coeffcent on vertcal ntegraton of approxmately a one day reducton n length of stay for every fve patents dscharged but contnues to be only on the margn of statstcal sgnfcance. 9 The nterpretaton of Table II Panel A s that hosptal vertcal ntegraton allows hosptals to dscharge patents to home health sooner relatve to non-ntegrated hosptals, but the effect s small representng savngs of only about 3% of bed-days and mprecsely estmated. Table II Panel B shows that the results on length of stay effects for hosptal vertcally ntegrated nto sklled nursng facltes are larger and more precse compared to vertcal ntegraton nto home health. Wthout controls, the correlaton between vertcal ntegraton and length of stay s -0.20, (column 1), and s precsely estmated. The full set of patent, hosptal and market controls soak up more varaton n the data, but have only a small mpact on the coeffcent on vertcal ntegraton (column 2). Column 3 shows the matched sample estmate. Matchng exactly based on all observable characterstcs of patents, hosptals, and markets yelds a precsely estmated pont estmate of Fnally, columns 4-I and 4-II show the two stages of our nstrumental varables analyss. Column 4-I shows that ncreasng the extent of vertcal ntegraton n a local market by 1% ncreases the probablty that a focal hosptal wll be vertcally ntegrated by 0.32%. The nterpretaton of the pont estmate of on vertcal ntegraton s: hosptals that are vertcally ntegrated nto sklled nursng facltes are able to reduce patent length of stay n the hosptal by one day for three out of every four patents who eventually receve post-acute care at a sklled nursng faclty, a reducton n total bed-days of about 11%. Table III summarzes the tests of the relatonshp between ntegraton and the ntensty of home health care provded to patents who are admtted to home health. Dscharges from vertcally ntegrated hosptals to ther own home health agences ( wthn frm transton ) receve an addtonal vsts/day, relatve to the baselne 9 We obtaned qualtatvely smlar results, usng 2SLS wth frst stages at the patent and hosptal level. 19

21 rate for patents dscharged from non-ntegrated hosptals, whle patents dscharged from ntegrated hosptals to external non-afflated home health agences had fewer vsts per day compared to the baselne (column 1). The F-test on the dfference between wthn frm transtons and external transtons from vertcally ntegrated hosptals s sgnfcant at the 1% level, whch suggests that wthn frm transtons are more demandng on the downstream organzaton relatve to market transtons. Controllng for whether external dscharges go to other ntegrated agences or to non-ntegrated agences and for dscharges from non-ntegrated hosptals to vertcally ntegrated agences wth a more refned set of nteractons has lttle effect on the man result. After matchng and ncludng the full set of nteractons, the pont estmate on wthn frm transtons s 0.01 or one addtonal home health vst per 100 day epsode. 10 Wth an average length of a home health epsode around 33 days, ths suggests that one of every three patents experencng a wthn frm transton gets an extra home health vst. Increasng one home health vst for one of every 3 of the 400,000 home health admssons per year that come drectly from hosptals would have ncreased total costs by about $13 mllon, assumng the average home health vst costs approxmately $100. Under prospectve payment, these costs are borne by the agences rather than by Medcare. The hgher speed wth whch ntegrated hosptals dscharge patents and the relatvely greater severty of patents health at admsson to ther home health agency rases an mportant publc polcy queston. Are vertcally ntegrated hosptals delverng lower qualty care by dschargng ther patents scker and qucker? Or do hosptals use ntegraton to ncrease ther effcency whle holdng qualty of care constant as we predct n our thrd hypothess? To answer ths queston, we test n Table IV whether health outcomes dffer between ntegrated and non-ntegrated hosptals for patents dscharged to post-acute care by regressng ntegraton on ncdence of rehosptalzaton. We fnd that n home health the correlaton between ntegraton and rehosptalzaton s ndstngushable from zero n full-sample OLS regressons (column 1), as well as n matched sample (not shown) and 2SRI tests (column 2), suggestng that under ntegraton nto home health, patent recovery tasks are shfted downstream wthout meanngfully affectng qualty of care. Column (3) shows that rehosptalzaton rates for patents dscharged to sklled nursng facltes wthn a vertcally ntegrated system are 0.6% lower compared to patents dscharged to sklled nursng facltes from non- 10 We obtaned smlar results usng propensty score matchng. 20

22 ntegrated hosptals. Whle the coeffcent s precsely estmated, the effect s small economcally compared to a baselne rehosptalzaton rate of approxmately 20%. However, after adustng for the endogenety of vertcal ntegraton usng 2SRI the pont estmate on vertcal ntegraton ncreases to -2.1%. The nterpretaton s that ntegraton actually leads to mproved health outcomes. The results suggest that whle ntegraton enables qucker and scker dscharges, the savngs obtaned are not the result of lowerng the qualty of care receved by patents. Hence, the costs of vertcal ntegraton are (presumably) borne admnstratvely. We close our emprcal analyss wth two caveats. Our emprcal approach reles on nterpretng the revealed preferences of hosptals, based on the assumpton that hosptal organzatonal decsons are made wth effcency crtera n mnd. Though our reveled preference approach s standard n the emprcal lterature on vertcal ntegraton (Joskow 1985, Hortaçsu and Syverson 2007), we cauton that we cannot estmate the costs and benefts of vertcal ntegraton drectly n our analyss. Second, whle the unque features of the health servces ndustry make t a partcularly appealng context for testng our theory of task algnment and temporal specfcty, t s reasonable to queston the external valdty of our fndngs. We beleve that the allocaton of tasks to assets s a fundamental determnant of temporal specfcty whenever the tmng of exchange s mportant, but leave the ssue open as an opportunty for future research. These caveats asde, the results suggest that vertcal ntegraton creates economcally meanngful opportuntes for hosptals to dscharge patents earler and n worse health to home health agences followng hosptalzaton. We nterpret the results as evdence that ntegraton allows frms to solve temporal specfcty problems by algnng tasks wth assets more effcently. Our fndngs do not dspute the dea that vertcal ntegraton ncreases admnstratve costs, such that, t may be superor to market exchange only for some hosptals (.e., the ones that choose to become ntegrated). Nevertheless, the results pont to one of the heretofore underapprecated advantages of vertcal ntegraton control over the allocaton of tasks to stes or assets. 7. Concluson Ths paper proposes and tests a smple theory where ntegraton addresses temporal specfcty problems by solvng task msalgnment problems. In our framework, we demonstrate how the allocaton of general tasks to 21