Procurement and Productivity: Evidence on the Cold Case of Public-Private Partnership

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1 Prourement and Produtivity: Evidene on the Cod Case of Pubi-Private Partnership Vinenzo Moisi May 11, 2017 Abstrat In the ast two deades, pubi authorities have inreasingy resorted to pubi-private partnership (PPP arrangements for the deivery of pubi servies. Under a PPP, the private ontrator is in harge of buiding the infrastruture, as we as managing and maintaining the faiity. Instead, under traditiona prourement the onstrution and operation phases are separated and reguated by two dierent ontrats. Reying on data oeted from the Itaian Distrit Heating industry, I empiriay evauate if dierent forms of ontratua arrangements indue dierenes in the tehnia eieny of rms due to herogeneous eves of apita quaity. I nd that the PPP ontrat aows a tehnoogia externaity bween the dierent phases of a projet to be internaized eading to a positive eet of PPP ontrats on TFP. In partiuar, a unit inrease in the apita quaity proxy shifts up the output of PPP rms by 15%. JEL Cassiation: H54 H57 O30 L11 D86 Keywords: Industry Produtivity, Contrating out, pubi-private partnerships, pubi-servie provision. PH.d. student at University of Rome Tor Vergata, DEDI Department, Fauty of Eonomis and attendant at EIEF graduate program, vinenzo.moisi@gmai.om. I wish to thank Kenio arbosa, Maro uso, Franeso DeCarois, Leonardo M. Giurida, Eisabta Iossa, Martin Padam, Arie Pakes, Giuia Pavan, Andrea Pozzi, Gabriee Rovigatti, Phiippe Shröder, Vaerie Smes, Friederih Wrazinsky and seminar partiipants at GSE Jamboree and EARIE 2016 for the hepfu omments. This paper was previousy iruated with the tite The Impat of Pubi-Private Partnerships on Produtivity of the Itaian Distrit Heating Industry. A remaining errors are mine. 1

2 1 Introdution Pubi-private partnership (PPP is being inreasingy empoyed for the provision of pubi utiities ike transportation, energy, IT servies and waste disposa. In the ast two deades, pubi authorities have reguary resorted to PPP arrangements for the onstrution and operation of infrastrutures. A PPP invoves the bunding of these two phases whih are typiay ontrated out to a onsortium of private rms inuding both a buiding and a faiity-management ompany. The bunding of these two phases into a singe ontrat is the essene of a PPP prourement and what dierentiates it from traditiona prourement where the onstrution and operation phases are separatey reguated. Contrat Theory iterature has provided severa ontributions anaysing the inentives for ost redution and quaity improvements of infrastruture under PPPs. Hart (2003, ennt and Iossa (2006, Martimort and Pouy (2008 and Iossa and Martimort (2015 isoate onditions for bunding to be optima in the presene of a vertia tehnoogia externaity. When the externaity aross stages is strong enough to os the ost of its own internaization, these studies show that bunding indues the ontrators to ook at the ongterm performane of the ass (the so-aed whoe ife ass management onept. This, in turn, bosters the ontrators' inentives to invest in ass quaity. Martimort and Pouy (2008 provide an exampe through the ase of the Amerian iruar prisons. The partiuar design of these buidings faiitates the work of prison oers by reduing the eve of abour inputs required to ontro prisoners. The existene of a positive (negative externaity impies that improving the apita quaity an redue (inreases the rm's margina ost at the operation stage. However, there is no empiria evidene doumenting the impat of PPPs on the produtivity of rms. Furthermore, many ase studies do not nd ear evidene of management osts redution or servie quaity improvements. 1 In this paper, I deveop an empiria mode to estimate tehnoogia eieny after ontroing for the apita quaity indued by PPPs. The main ontribution is to measure how muh tehnoogia eieny responds to a variation of the apita quaity due to the prourement sheme. A strutura approah is meant to rrieve a reiabe proxy for the unobserved produtivity term. For this purpose, I study the Itaian Distrit Heating industry (hereafter DH. A DH is an integrated nwork aimed at generation and distribution of therma energy through a system of pipes and heat ex-hanger substations. The DH embodies the perfet industry to observe the externaity eet bween the onstrution and the operation phase. In fat, the pipeine's design needs to be arefuy panned in order to redue exessive osts from future enargement and onnetions works, as we as to preserve 1 See Iossa and Martimort (2015 for a daied ist. 2

3 the therma apaity of faraway nodes. In this setor, traditiona prourement invoves a serious probem of mora hazard. When the ayout is hosen by ompany A, but the ost of providing energy is arried by ompany, ompany A does not internaise the redued future margina ost from ower heat osses. Then, ompany A nds optima to shirk on its deivered quaity of the infrastruture. This resuts in higher operating osts for ompany. However, when a onsortium both onstruts the pipeine and provides the servie, it wi aount for the redued margina ost of providing heating in the onstrution stage. A prourement sheme, as PPP, whih ompes rms to temporariy join in a onsortium, rereates the onditions to internaise this externaity and to sove the mora hazard. I show that a positive externaity exists in this industry and I measure the produtivity eets of PPP ontrats on DH rms. Using spei funtiona forms for prodution, I bak out estimates for produtivity and estimate its response to the spei award mehanism used. In presene of a positive externaity not impementing PPP impies a ower eve of wefare, sine rms oud produe more eienty at a ower margina ost. Aternativey, in presene of a negative externaity impementing PPP woud be drimenta. PPP was heaviy debated: it was seen unti a few year ago ony as a soution to keep investments high, despite redued pubi budgs. I am the rst to show that PPP works propery in an industry with harateristis in ine with the assumptions stated in the iterature. A pubi authority whih knows beforehand the gains/osses in term of tehnia eieny oming from PPP wi have bter guidane in the use of this prourement too. Furthermore, this paper provides more evidene on how pubi prourement an aet produtivity. PPP is proved as Fixed pries and Cost Pus ontrats, see Gagnepain and Ivadi (2002, to be a driver of produtivity. My resuts show that apita quaity has a positive and signiant impat on PPP rm's produtivity. I nd a non signiant margina eet of our proxy for apita quaity for not PPP rms. There is, in turn, a strong and highy signiant margina eet on output for PPP rms. In partiuar, inreasing by one unit the measure of quaity shifts up the expeted hange in og of output by for PPP rms. In eve terms, it orresponds to an output inrease of 15%. In partiuar, this eet is signianty strengthened in the presene of a PPP ontrat. I report a signiant positive eet of the PPP dummy of 0.128, whih in eve terms orresponds to a 14% inrease in output. Moreover, the estimates of the prodution funtion's paramers indiate the presene of dereasing rurns to sae in the tehnoogy. This work utiises a unique datas on the universe of Itaian DH faiities bween 2007 and For eah pant, I an observe aurate information on the physia quantities of output and inputs. Physia data are usuay diut to rrieve. Athough, they are 3

4 essentia to orrety identify prodution funtion sine they avoid omitted prie bias in estimates, see Tybout (2000. I an use this information to onstrut a reiabe proxy for the apita quaity. This is dened as the negative (- ratio of the tota ength (m of the pipeine to the tota amount of heated voume (m 3 and is measured as the needed m of pipeine every 10 2 m 3. This paper reates to three dierent strands of iterature. First, I ontribute to the ited iterature on PPP with an empiria test for the preditions of these modes. Moreover, this paper is reated to the ontribution of Gagnepain and Ivadi (2002 and Gagnepain a. (2013, sine it is an additiona evidene on how prourement sheme an aet produtivity. Seond, This paper reates to the path breaking resuts by Oey and Pakes (1996, Levinsohn and Prin (2003 and Akerberg a. (2015. Their strutura approah based on the timing of assumptions governing the rm's prodution proess is meant to sove a probem of simutaneous endogeneity, see Kte and Griihes (1996. The apita quaity is usuay an unobserved state variabe for the rm. This means that tehnia eieny is not the ony variabe unobserved and any attempt of orret identiation through strutura approah resuts invaid. Third, I ontribute to the ongoing debate on produtivity assessment. I rrieve a hanne trough whih the prourement sheme aets the produtivity of rms. In fat, arge dierenes in produtivity aross pants are usuay observed in the same industry. artesman and Doms (2000 nd many ases where the highest produtivity rm has more than twie the measured produtivity of the owest produtivity rm. Fox and Smes (2011 observe that the mean ratio of the 90th quantie of produtivity to the 10th quantie of produtivity is of 3.27 aross eight Danish manufaturing and servie industries. Moreover, iterature fouses on the fat that piees of apita equipment are of dierent vintages, see (Whean, 2002, and mahines ose their vaue due to tehnoogia progress. aasubramanian and Sivadasan (2009 nd that inreases in apita resaebiity are assoiated with a redution in produtivity dispersion. Then, apita quaity seems of great onern reative to tfp dispersion. The remainder of this paper is strutured as foows. In Setion 2 of the paper, I present the DH setor, highighting the prevaene of PPP arrangements in this setor. In setion 3, I desribe in more dai the main data soures. In Setion 4, I review two branhes of iterature, PPP ontrat theory and produtivity. In Setion 5, I introdue the empiria framework. This wi be foowed by the spei eonomri strategy to identify the oef- ients of the mode. Finay in Setion 6, I present the resuts from the estimation of the mode. 4

5 2 akground A DH is an integrated nwork system buit under pubi authorization in servie of a urban neighborhood. The pants are aimed at distribution of therma energy and o-generation of eetri energy. The eetri energy produed is ompitivey sod to the nationa mark and the therma energy is fuy redireted to the urban neighborhood. DHs have the right to serve a neighborhood of dimension stated in the ontrat by the pubi authority. The therma energy produed in o-generation is not suient to satisfy the needs of the nwork, then auxiiary boiers, whih produe ony therma energy, satisfy the residua demand. We aways observe an auxiiary boier working, meaning that there is no free disposibiity of the therma energy.this impies that eetri energy prodution is onstrained by the therma energy demand. Moreover, given the onstant physia reation bween eetri energy and therma energy prodution DH is usuay onsidered as a singe produt industry and eetri energy as a residua, see rã nnund and Kristrà m (1999. DH rms stipuate ontrats of servie with the ustomers of the nwork and eah househod oud be served ony by a DH nwork. As a onsequene, DH rms are oa monopoists. However, a reent study of The Itaian Compition Authority (ICA suggests the rare ourrene of extra-prots in Itaian DH setor. Sine househods an insta their own heating systems and this outside option has a ost of instaation, DH rms optimay prie heating at the prie of instaing an autonomous boier pus the ost of produing heating with it. Therma energy distribution is arried out through a nwork of pipeines, that transport a heated vehie and onnet severa heat exhange substations. Eah substation onnets the main nwork pipeine to the buidings. A singe node an serve a ertain amount of therma power to the urban neighborhood. Transporting therma energy to househods impies heat osses over the traveed distane. DHs dea with a trade-o bween having more nodes or a shorter nwork of pipeines. Thus, an optima ayout beomes ruia in order to preserve temperature and pressure of the vehie. PPP sheme is usuay used in substitution of a omped tender for onstrution and a pubi onession for the operation of the pant. In the ast deade, PPP has represented the 13% of the ontrats in the DH setor and the 35% in terms of the vaue of the entire mark, SIOP (2013. The same study evauates DH as a growing setor (as far as PPP, mainy in the more reent period. 5

6 3 Data I an expoit an origina datas on DH industry in order to test and quantify the eet of PPP on produtivity. These data are reeased every year by the Airu, the Itaian assoiation of DHs and onern a tota of 148 pants, bween 2007 and 2014, mosty the entire popuation, mainy distributed in north Itay. For eah pant, I observe aurate information on output in terms of therma and eetri energy (mw h produed and buidings' heated voume (m 3 every year. The therma energy distributed is the main output variabe in the mode. Moreover, we observe the amount of heat osses (mw h, whih it is the intermediate materia and the proxy variabe in the strutura mode. On the other hand, I use buidings' heated voume (m 3 every year quarties to onstrut rm size dummies. I added these dummies, primariy, to x the heated voume and be abe to interpr apita quaity in a meaningfu way. Moreover, these dummies ontro for big shifts in therma apaity of DH rms. Furthermore, the datas shows usefu information on the inputs. Two proxies of apita are avaiabe, the ount of heat ex-hanger substations, whih distribute therma energy to buidings, and the ength of the nwork pipes measured in m. The former is the proxy for the apita input and presents some herogeneity sine the heat ex-hanger substations dier in terms of therma apaity. Assuming a onstant temperature of operation, I use the rm size dummies to ki this kind of herogeneity. Other aspets reated to apita's quaity may inuene the DH's distribution proess and the ength of the pipeine is empoyed to onstrut a apita quaity proxy. I investigate for a mehanism trough whih PPP inuenes the quaity of the infrastruture. In order to rrieve a proxy for the apita's quaity, I expoit the nwork nature of the DH's apita. Capita quaity, a, is given by the negative (- ratio of the tota ength of the pipeine to the tota amount of heated voume a = pipeine s egnth heated voume and measured as the needed m of pipeine every 10 2 m 3 heated. Dereasing vaue of this index shoud have a positive impat on output sine heat osses (that derease the tota therma energy distributed are physiay orreated to the average ength of the pipeine. Note that theoria iterature suggests that under traditiona prourement the buider has no inentive to s the optima eve of apita's quaity not exerting enough eort in the design of the faiity. Under PPP, sine the operator is invoved in the buiding's design phase, she an state the optima eve of apita's quaity design she needs. A s of dummies whih indiate some key dierenes in DH tehnoogies are introdued in the mode. First, I ontro for the therma vehie used, steam or heated water, whih 6

7 an make a dierene in the rate of dispersion. Seond, the majority of pants produe in o-generation therma energy and eetriity. Produing therma energy ony has severe impats on the na dimension of the rm. I am abe to observe the therma energy impied in the distribution proess in term of megawatt per hour (mw h and the heat osses of the pipeine. I use heat osses as intermediate materias instead of the whoe therma energy impied. This separate the therma energy deivered from the therma energy direty reated to the distribution proess. y using homogeneous input greaty simpies the anaysis sine a singe input is onsidered in pae of severa propeants impied in the prodution proess. Moreover, there are important demand shifters whih inuene prodution deisions of DH rms. First, geographia dummies are introdued to ontro for dierene in average temperature bween dierent areas. I onstruted three main geographia zones expoiting a therma energy index referred as heating degree-days (abbreviated as GG from the Itaian version of the index used to assess the energy used for spae heating in buidings. This measure was introdued by European standard EN ISO and dened as: GG = d (20 T e 1 where d is the number of days of the onventiona heating period and ranges bween 90 and 365; 20 Cesius degree is the onventiona ambient temperature in Itay; T e is the daiy average outer temperatures. A ow vaue of GG indiates a short period of heating and daiy temperatures near to the presribed temperatures for the environment. The three zones are onstruted based on imati bands dened by Itaian aw and Zone 1 is omprised bween GG, Zone 2 bween GG and Zone 3 above 3000 GG. Seond, I introdue a ontinuous variabe whih measures the amount of therma energy extrated by the avarage buiding. I expoit the perentage of Cesius degree dierene in inoming and outgoing water's temperature. This dierene is usuay used in engineering iterature and the index is a standardized measure of average therma energy dispersion and athes shifts of the heating demand due to therma isoation of houses. In order to identify the pants onstruted under PPP, I expoit a researh pubished by Siop and the Chamber of Commere. I aount for a tota of 25 projets in exerise reaized using the PPP bween 2002 and Finay, I integrate data on the number of workers direty oeting them from the baane she of eah ompany. These data refer to fu-time bue oars. In tabe 1, I report seeted desriptive statistis of the entiry of rms aong with those for eah group, PPP or not. The average heated voume for Itaian DH rms is around 7

8 m 3. Ony 24% of not-ppp rms do not produe eetri energy, whereas amost the whoe PPP sub-sampe, 95%, produes in ogeneration regime. 44% of the entire sampe use heated water as a therma vehie over steam. The average temperature extrated is Ceius degree and buidings served by PPP are more energy eient of 1 degree. PPP rms are mosty oated in Zone 2 (85% and show smaer vaue (higher quaity of the apita quaity proxy. (1 (2 (3 whoe Firms no PPP Firms PPP Firms Tota energy, mwh Heat Energy ost, mwh Number of Workers Nwork Length, m Heat Exhanger Substations Heated Voume, 1000xm Quaity Design, m/100xm ween GG ween GG Above 3000 GG Cogeneration Heat vehie: steam Average Temp extrated, ï ½ Tabe 1: Summary Statistis 4 Literature review 4.1 PPP iterature review The rst two papers that investigate the eets of pubi-private partnership are Hart (2003 and ennt and Iossa (2006. These papers buit on Shmitz (2005, who ss a prinipaagent mode in whih the prinipa deides how to organize a projet that onsists of two stages. In partiuar, Hart (2003 provides a sting where a buider impements two kinds of non-ontratibe investments, produtive and unprodutive. oth redue operating osts, athough ony the produtive investment inreases the ben of providing the servie. Under traditiona prourement, the buider has no diret advantage in terms of ben's inrease or ost's redution from impementing the unprodutive investment, nding optimay to exert too muh of the produtive investment, but the right amount of the unprodutive one. Under PPP, the buider party internaizes the externaity of his unprodutive investment 8

9 athough the eve of the produtive one remains too high. ennt and Iossa (2006 introdue a mode where investments are ex-ante non-ontratibe but ex-post veriabe. In suh sting, they study in depth the desirabiity of bunding projet phases and of assigning ownership to the investor. Ownership assigns the right to the owner to impement quaity enhaning or ost-reduing investment. The probem of keeping from optimay investing in the rst phase of the projet is ess severe under PPP when a positive externaity bween the buiding and managing phases exists. Furthermore, the authors show that pubi ownership imposes on government a ommitment to renegotiate and share with the investor the surpus from the impemented investments. Martimort and Pouy (2008 reaxes the hypothesis of non-ontratibe operationa osts and servie's quaity and rrieve resuts simiar to ennt and Iossa (2006's ones. In partiuar, they nd that granting ownership imperfety aigns inentives bween agents and the important point is not who owns the ass, but instead whher phases are bunded or not. Ageny osts are found ower under a PPP arrangement ompared with traditiona prourement, in presene of a positive externaity bween buiding and managing. Chen and Chiu (2010 introdue an interim ontratibiity framework and assume that the operation task beomes ontratibe subsequent to the buiding stage. Their resuts suggest that under private ownership, task externaity and task interdependene sti pays an important roe in shaping the trade-os bween bunding and separation. In partiuar, some degree of onvexity of the ost funtion, whih aows for task ompementarity, pays the interesting roe to favor the buider's ownership and disfavors the onsortium's ownership. Lasty, Hoppe a. (2013 onduted a aboratory experiment on PPP. The authors nd that a PPP provides stronger inentives to make ost-reduing investments whih may inrease or derease servie quaity. 4.2 Produtivity iterature review The most ommon approah in iterature to assess the produtivity of rms is reovering Soow's residua from some we-behaved prodution funtion: F (z i ; α exp(ω i + ɛ i (1 where ω is individua i produtivity, z i is a vetor of inputs and α is the vetor of margina produtivity of eah inputs. The error omponent ɛ is meant to apture both measurement errors and unobserved produtivity shoks. OLS issues in estimation of og-inearized version of equation (1 are twofod. First, the error omponent is orreated with z i beause rms expoit information on ω i in their deision 9

10 onerning inputs quantity. Kte and Griihes (1996 refer this endogeneity as simutaneity sine output and inputs resut as the soution of a simutaneous equations system. Seondy, data in physia terms are ommony not avaiabe. In pae of physia output and inputs eonomriians use proxies. Saes deated by an industry-wide prie index are ommony used in pae of output and baane she data as substitutes of inputs. Suh substitutions have no onsequenes under perfet ompition sine a rms observe the same pries. Instead, with imperfety ompitive marks estimated rm-eve produtivity is ikey to be misstated due to the demand shifters' eet passed trough pries to output and input's proxies. Sine the probem is originated by omitted pries, it is usuay referred as omitted prie bias. Mhods of soving the simutaneity probem inude nding instruments for inputs or assuming a xed over time produtivity and using a xed-eets estimator, Mundak (1961. oth mhods seem to have faied. Input pries have shown weak preditive power and the data an be diut to obtain. Moreover, impementing the xed-eets assumption woud not sove the endogeneity probems if hanges in produtivity are responsibe for hanges in input and quaity hoies. Oey and Pakes (1996 and foowing Levinsohn and Prin (2003 and Akerberg a. (2015 propose a soution in terms of a strutura approah whih expoits observed pant deisions as proxies for unobserved produtivity shoks. The intuition reies on the existene of a proxy variabe for produtivity whih reats to variations in the TFP. If this funtion is proved to be invertibe, then the inverse funtion an be estimated and pugged in the prodution funtion to ontro for endogeneity. Oey and Pakes (1996 isoate the proxy variabe direty from the investment dynami optimization probem of a rm, by inverting the amount of investment. From the dynami probem aso the terminoogy is inherited, suh that the variabes whih onstitute the minimum s of information in order to rrieve the poiy funtion (the stok of apita, the age of a rm,. are referred as dynami state variabes. On the other hand, inputs (abor, materias. whih an be modied in a suessive moment, after produtivity shoks our, are referred as stati free variabes. Investment as a proxy for the TFP presents an enormous probem in terms of data avaiabiity. Sine in many oasions investment assumes zero vaues, it beomes not invertibe in these points. Consequenty, many observations must be dropped out and the remaining sampe needs to be representative. Levinsohn and Prin (2003 propose a soution sighty hanging the timing of rm's deision. Supposing intermediate materias (energy, fues. are hosen bween the ourrene of the produtivity shok and the deision regarding free variabes (abor and eventuay others intermediate materias, they respond to produtivity and at as a proxy variabe The stati variabe intermediate materias do not suer from the 10

11 zeros probem and guarantee greater data avaiabiity. Akerberg a. (2015 point out how the hoie of free variabes (abor. may be a funtion of previous hoies in terms of state variabes. Consequenty, any attempt to estimate separatey free variabes oeients oud suer from a serious probem of oinearity. They propose to give up any attempt to separatey estimate the oeients and to estimate the whoe oeient vetor α non-ineary. The omitted bias probem, as highighted by Katayama a. (2003 onstitutes a serious probem whih invaidates many attempts of TFP estimation. Soutions invove onsidering a demand mode ike in De Loeker (2007 or reying on data in physia terms ike in this paper. 5 Mode 5.1 Theoria framework Under traditiona prourement, a pubi authority oud oer to the buider ( a ontrat suh that the payment sheme is τ + γ C with {(τ, γ } R [0, 1], where τ is a transfer from the authority and γ the perentage of ost (C shared with the rm. The ase γ = 1 orresponds to a ost-pus ontrat where the ontrator is fuy reimbursed for its own osts, whereas γ = 0 stands for a xed-prie ontrat, where the ontrator reeives a xed payment. Fixed prie ontrats are of ommon use for DH onstrution, then τ ony is ontratibe. The same pubi authority oud oer to the operator (O another ontrat suh that the payment sheme is τ O + γ O R O with {(τ O, γ O } R [0, 1], where α O is a transfer from the authority and γ O the perentage of unit revenues shared with the rm. A payment mehanism soey based on user harges orresponds to τ O = 0 and γ O = 1, so that the ontrator keeps a the revenues. On the other hand, payment mehanism based on avaiabiity orresponds to τ O > 0 and γ O = 0, so that the ontrator's reward is xed. DH rms oet revenues from ustomers ony and revenues annot be ontrated upon. Eah buider faes the probem to impement a minimum eve a R + of faiity's quaity, beow whih the pant does not work, and eventuay a quaity investment a i R ++, whih wi inuene the operationa ost of the operator and inreases the overa quaity of apita, a. 5.2 Mora hazard Suppose the foowing we behaved dierentiabe in every point DH's ost funtion: 11

12 with C(. a C(ED, a, e; 0, C(. 0 and C(. e ED apita quaity, a, whih redue the needs of eah input to produe the same eve of output. 0 The tota ost is a funtion of the eort, e, and the The eort, e, enompasses a these fators whih IO iterature has reognised as eetivey abe to redue rm unit ost, see Syverson (2011 for a ompe survey. This an be ike Gagnepain and Ivadi (2002's ut of ineieny in the pubi transportation setor due to the enforement of prourement ontrat on suppiers. Under traditiona prourement, the buider knows nothing about the ost struture of the operator, so impementing a partiuar quaity investment eve a i aets her own ost negativey. This ost of impementing a i is an unknown funtion g(a i with g(. > 0. Then, a i the buider's optimisation probem, who reeives a rst prie payment sheme, τ > 0 and γ = 0, woud be: max a i τ g(a i where the buider deides to optimay impement the smaest apita quaity eve, a, in order to make the pant working 2. Suessivey, the DH (the operator an exert an eort e in order to redue the input ineieny of her own ost C, whose impementing ost is the unknown funtion z(e with z(. 0. The optimization probem of the operator, who e reeives a payment shemes [τ O, γ O ] and takes a = a is: e = argmax e 0 τ O + γ O R O C(ED, a, e; z(e (2 In a PPP, a pubi authority oers to the buider and the DH, joint in a onsortium, a unique ontrat. The optimisation probem is: ( a P P P, e P P P = argmax a i, e 0 τ + γ R C(ED, a, e; z(e g(a i (3 whih deivers the foowing apita quaity eve and eort investment: 2 A FP ontrat wi not dermine a quaity investment, a, if the quaity investment is not impement as a reduing uider's ost eort. A dierent payment sheme inked on the quaity investment provided by the buider obviousy dermines some quaity investment impemented aso under assia prourement. 12

13 a P P P := a + a i P P P e i P P P := ep P P e Under traditiona prourement, the eve of apita quaity impemented annot exeed the eve of quaity under PPP, whih means that the tota eve of apita investment a i P P P is s at zero. The optima apita quaity inreases when the gain from inreasing the apita quaity through investing C(. is not neutraized by the ost oss term, z(.. The eet on a i a i the tota eve of eort is ess ear, sine it is reated to onvexity of the ost funtion, trough the ross derivative C(.. When C(. > 0, we shoud observe substitution bween the tota a i e i a i e i eve of eort and the apita quaity. I do not have any hint about the true diretion of the ross derivative, but I an rey on the ontro funtion approah to ontro for suh eets. In appendix A, I propose an expiit soution under the assumption of a obb-dougas ost struture and exponentia ost of impementation. of a and e. 5.3 Empiria mode I assume the foowing DH rm's singe-output strutura vaued-added obb-dougas prodution funtion: ED = Ω (a, e K α L α where ED, K, L are respetivey output, apita, abour. Ω (. is the unobserved term for produtivity, whih resuts ruia for the identiation. In partiuar, ED is the mhwh of therma energy deivered. Firsty introdued by Gandhi and Rivers (2014 and empoyed by Akerberg a. (2015, this speiation suppose proportionaity bween intermediate materia, ET, and output, ED 3. In partiuar, ET is the therma energy impied to over heat osses and pays a main roe in the empiria mode sine it is my proxy variabe for produtivity estimation. Under traditiona prourement rms impement the ower apita quaity eve a. On the other hand, PPPs indue rms to make a quaity investment a i P P P. The foowing expression 3 The strutura vaue-added prodution funtion is direty derived from the foowing DH rm's singeoutput gross output Leontief prodution funtion: ED = min {Ω K α L α, α ET } (4 The intermediate materias, ET, are onsidered proportiona to the output. After ontroing for apita quaity and other imati and environmenta fators suh hypothesis seems pausibe sine a physia onstant exists bween the amount of heat oss and the pipeine ength. 13

14 denes the tota apita quaity impemented by a DH rm (onsidering both PPP and not PPP : a = a P P P P P P + a (1 P P P = a + a i P P P where P P P is a binary variabe to identify PPP pants. Seondy, based on the urvature of the ost funtion PPP rms adjusts the operating eort, e, given the quaity design investment, a. Simiary to the quaity, I an dene the tota eort, e = e P P P P P P + e (1 P P P = e + e i P P P The two prourement sheme give rise to two separate tfp funtions for PPP and not PPP rms 4. Suppose these two funtions ω notp P P and ω P P P are at east C 1 and ω it is an unobserved produtivity shok term. Taking a rst order Tayor expansion of ω notp P P and ω P P P in (a, e and oeting PPP and not PPP rms, I obtain: [ ] [ ] ω not P P P (a, e ω P P P (a e ω(a, e a it + ωnot P P P (a, e a it P P P + a it a it a it }{{}}{{} β a β int + [ ω(a e P P P ω(a e not P P P ] }{{} β P P P P P P (5 where the onstant omponents are omitted for sake of simpiity. Pugging ω(a, e into the inearized Cobb-Dougas prodution funtion, equation (4, the redued form mode for a DH rm i in time t an be written as: ed it = α s k it + α it + β a a it + β int a it P P P i + β P P P P P P i + ω it + ɛ it (6 where sma ases stay for ogs of output and input variabes. The unobserved terms reative to e it are absorbed inside ω it aong with the others unobserved fators whih inuene produtivity. The idiosynrati error ɛ it aounts for measurement error. The oeient β P P P shoud be interpred as the average PPP additiona eet on TFP, whih is the mixed eet of trading o quaity investment and operationa eort. The interation term β int is the inrementa eet of a unit inrease of apita quaity when a rm is buit and operated under PPP. This shoud be interpred as the externaity eet on produtivity. On the 4 In this ase the points ( a P P P, e P P P and (a, e identify two singe points in just as many tfp funtions. In Appendix A, I paramrize the domain of this two funtions through two exogenous paramers δ, κ [, + ]. These paramers apture the externaity eet of apita quaity and abour eort. 14

15 other hand, the oeient β a measures the overa margina eet of the apita quaity a it. The identiation of β int and its interpration as the eet of the tehnoogia externaity is based on a simpe feature of the inear mode. Introduing size dummies, S it, for the quartie of the heated voume m3 I avoid variation in the quaity index due to variation of the heated voume. In this way, hanges in this index are ony due to hanges in the pipeine's ength. In addition, the mode aounts for others ontro variabes, Xit, ontroing for tehnoogia and suppy shifters: ed it = α s k it + α it + β a a it + β int a it PPP i + β PPP PPP i + S it ρ s + X it ρ x + ω it + ɛ it For sake of simpiity, I oet a the other ontro variabes in a matrix X it, oapsing the mode to: ed it = α s k it + α it + X it ρ + ω it + ɛ it As aready pointed out in the review part, estimates of equation (6 by OLS wi inur the we-known endogeneity probem assoiated with estimating prodution funtions: the presene of ω it (e it being possiby orreated with pant's apita, abour and materia demand. In this industry, produtivity's dierenes may be owed to unobserved dierenes in quaity of inputs as we as to previousy unobserved dierenes in pant's harateristis due to the form of prourement used to reaise the pant. In order to aount for endogeneity, I adapt the Levinsohn and Prin (2003's approah orreted by Akerberg a. (2015 to the DH industry introduing a new ontro variabe for the apita quaity and ontroing for PPP eet. First, I speify the inputs timing deision and the stati optimisation probem of a DH rm, in order to identify amongst proxy variabes the state variabes from the free variabes. Seond, I identify the input oeients expoiting the identied information s at time t. 5.4 Identiation The main probem for identiation is the endogeneity due to simutaneous output and inputs. In this ase, identiation is obtained through a strutura mode expoiting the timing assumption behind DH rm's dynami optimisation of prots. Moreover, the possibiity to rowd out intermediate materias demand through a Leontief prodution funtion avoid 15

16 oinearity issue due to the estimation of intermediate materia input eastiity Timing assumptions A DH pant hooses the amount of intermediate materias based on its stok of apita, k it, abor, it and a vetor of observabe harateristis of the pant, x it. This vetor of observabe harateristis of the pant, x it, ontains information about the tehnoogy, demand and, as hypothesized in this papers, prourement shifters whih aet the optima eve of apita quaity of the nwork, a it. The deisions unfod as foows: 1. Output hoie made: a pant's manager begins the period knowing the urrent eve of apita, k it. The pant's manager aso observes ω EF ORE it, beief on produtivity this period given the information s at the beginning of the period, whih is aso funtion of the eort e, the quaity investment a and a vetor of other observabe ontro variabes. Consequenty, reying on this information s a pant's manager deides the targed eve of output. 2. In an intermediate period bween output hoie and prodution, DH rm's manager deides the amount needed of abour inputs, it. Note how abour is not a perfety variabe input deided at the time prodution takes pae, the above timing of input deisions impies that abour is a ess variabe input than intermediates, sine abour is hosen one sub period before produtivity shoks our. 3. Prodution ours. ased on its hosen targs, the pant arries out its distribution ativity and observes reaised outomes for output and osses of the nwork. The DH AF T ER rm's manager aso updates his knowedge about its produtivity, ωit. 4. Intermediate inputs hoies. During prodution in a dynami proess, the pant's free variabes are adjusted to reet what has been earned about produtivity, the information s I it = (k it, it, x it, ω AF T ER it pant deides on intermediate inputs, it ; 5. New period deision. is updated. With this information, every 5 As highighted by Gandhi and Rivers (2014, the Leontief form oud be not suient to guarantee the identiation of the eastiities paramers. To understand, suppose K it and L it are hosen before ET it and the prie of ET it suddeny varies suh that revenues do not over the ost of the intermediate materia required to produe that output. In this ase, DH rms woud not generay hoose ET it to satisfy ED=α ET= Ω K α L α, and thus the data oud ontain points where prodution is equa to zero. Athough, this doesn't appear as a big probem. Sine DH rms wi either satisfy ED=α ET= Ω K α L α or produe 0 output, and if they produe zero, they wi presumaby not be in the datas of those operating and thus it is not a probem for estimation. 16

17 Considering the evoution of the proess up to now, it is reasonabe to mode the pant's expetation of produtivity as an exogenous Markov Proess, EF ORE ωit = E[ω AF T ER it I it ] = E[ω AF T ER it AF T ER ωit 1 ] As expetations on produtivity at t are formed, the pant hooses whher to remain ative in the mark in period t, and if it is so a new ye starts. AF T ER I assume as in Pakes (1994 that the proess is stohastiay inreasing in ωit and that the ω it moves aording to an exogenous Markov proess. Produtivity ω it onsiders the entire of unobserved fators whih an modify the voume heated by a DH rm, one observabe harateristis and quaity are kept onstant Firm's Stati optimization probem I foow the exampes of Oey and Pakes (1996, Levinsohn and Prin (2003 and Akerberg a. (2015 soving ony the stati prot maximisation probem, whih is suient in order to identify the prodution funtion paramers. After prodution ours, the pant updates its beiefs about its produtivity and it wi observe the new variabe: ωit A = ωit + ɛ ω it (7 I assume that (ɛ it, ɛ ω it are mean zero and unorreated with the information avaiabe to the pant, athough the omponents of this vetor may be orreated with eah other. eause the pant wi not earn about (ɛ it, ɛ ω it unti it operates, it has to optimise its output hoie under unertainty. The pant hooses its expeted output to sove the foowing stati prot maximization probem: π(k it, ET it, L it, ω it, x it = max it, it, E[P ED ED it (ET it P K K it P L it ] s.t. ED it = F (K it, L it, ωit x it Lasty, the foowing emma estabishes that the intermediate materias demand, ET it is strity inreasing in produtivity, whih it is a suient ondition for the invertibiity, and aows to use intermediate materias demand as a proxy for produtivity in our estimation strategy. The foowing is proved in appendix : Lemma 1. The pant's intermediate materia demand, it, is strity in- 17

18 EF ORE reasing in ωit if the foowing ondition on the prodution funtion hods: ( ET L ET ωit ET ωit L df ηf det ω it L 2 d 2 F ET ωit dl L ET L ωit L df det L ω it > Seetion onerns uyers do not invove seers in disussions before the ontrat awarding if a diret negotiation is not used to seet the seer. A rm's expertise to dea with a partiuar form of ontrat or to enfore the pubi body's hoie of this partiuar ontratua form may be an issue. In presene of this form of seetion, the eet of the PPP on the DH rms' performane oud be the resut of the seetion of a partiuar sub-sampe. In order to avoid suh onerns, I onduted a preiminary mark anaysis. I expoit tender awards data to assess the dynami of rms' mark shares. Seven rms represent the 56,51 % of the entire PPP mark (tabe 4. Conversey, the same seven rms (Cofey and Siram are onneted aount for the 47,53 % of the not-ppp mark (tabe 5. Confronting PPP with not PPP projets, rms seem to rain their reative mark share. PPPs and not PPPs are not direty omparabe in terms of awards, sine the former bundes dierent tasks. Suh herogeneity oud indue some restritions to ompition amongst DH rms, whih transates in seetion: some sma rms annot ompe in very big tenders. The poor / good outome of PPP pants oud be again the resut of seetion of big / sma or ow / high quaity rms. In order to hek, I anaysed a sampe of 33 tenders in the period (earier data were not avaiabe. In tabe 6, you an ompare the average number of bids made in PPP tenders with the average number of bids for buiding, operating and maintenane tenders. In this ase, the number of bids proxies the eve of ompition in partiipating in the tender, the same number of bids attains to the same eve of ompition. The average number of bids for a PPP tender is 4,08 with a standard deviation of 5,99 (right oumn in tabe 6. The average number of bids for a not PPP tender is 5,39 bids with a standard deviation of 2,85 (eft oumn in tabe 6. A non diretiona t-test (t-statis equa to 0,77 with 31 df onrms that the dierene bween the means of two independent sampes is not statistiay dierent from zero. Finay, uso a. (2016 use a database on frenh tenders and nd a positive reation bween tightness of Pubi ody's budg onstraints and the use of PPP. This nding strengthens my point of PPP's eet being exogenous to rms' manipuation. 5.5 Estimation Pugging identity equation (7 into mode equation (6, it an be rewritten as: 18

19 ed it = α s k it + α it + x it β + ωit A ɛ ω it + ɛ it The vetor x it = [a it, P P P i, a it P P P i, D i, Cog i, T eh i, dt emp it, S it, 2014 t ] ontains a the reevant ontro variabes for the DH's distribution proess. The P P P i identies PPP pants. The D i vetor inudes a the geographia dummies. The Cog i dummy ontros for pants in ogeneration regime. A teh dummy, equa to 1 for heated water, is inuded to ontro for tehnoogia dierenes in the physia state of the therma vehie (heat water, steam. The dt emp it variabe is the ontinuous index whih measures average therma dispersion of buidings. The S i vetor inudes rms size dummies. The 2014 t is a dummy I added to ontro for partiuary hot 2014's winter. The vetor (ɛ ω it ɛ it does not raise any endogeneity probems. These vetor is reveaed to the DH rm after it makes its input hoies and it is unorreated with the rm's information s at the time output hoies are made. On the other hand, DH rms' expetation about ωit A is a funtion of ωit, whih fores to ontro for ωit A sine it (ωit is aso a funtion of ωit. From Lemma 1, DH rm's expetation about its produtivity an be reovered by inverting the series of intermediate materias hoies suh that ω A it = 1 it ( it, k it, it, x it (8 I foow Levinsohn and Prin (2003 and Akerberg a. (2015, substituting 8 into the prodution funtion in order to obtain the rst stage equation: ed it = α s k it + α it + 1 it (k it it it x it ɛ ω it + ɛ it = Φ(k it it it x it + ε it (9 where Φ is a poynomia in (k it, it, it, x it. In order to prevent oinearity issue, oef- ients are not identied in this step. First stage is meant to g rid of the error omponent, ε it = ɛ ω it + ɛ it, and obtain the sampe ounterpart ˆΦ, from non paramria estimation of equation (9. Under the LP assumptions and at the true vaue of the oeient vetor (αj, βx with j =, and x = a,..., D 1,.., D n, t, ˆΦ oud be used to reover a reiabe proxy of the produtivity ω it, then ω it is auated as: ˆω it = ˆΦ it α s k it α it α it x it β I onsider a proess where agged eve of apita quaity is aowed to impat produtivity 19

20 of PPP rms and thereby aets produtivity hanges as : ω it = g(ω it 1, a it 1 P P P it 1 + ξ it i.e. the produtivity foows a rst order markov proess, where g is a non-paramri funtion of ω it and a it 1 P P P it 1. This aptures produtivity hanges due to ative investments based on the apita quaity eve of a PPP rms. When PPP rms update their expetation to higher produtivity eve and have to deide hanges to the apita stok, then they adjust their apita in order to keep the optima apita quaity. The term, ξ it, is a shok to produtivity bween time t 1 and t, whih is independent of the DH rm's time-t information s. The sampe ounterpart of the poynomia g(. is reovered by regressing non-paramriay ω it on a poynomia of ω it 1, whih is used to identify the series of shoks ξ it = ˆω it ĝ(. Finay, expoiting the timing assumption, you an onstrut a moment estimator using the foowing s of moments: E ξ it it 1 ξ it k it ξ it a it ξ it a it P P P i ξ it P P P i ξ it Di n n = 0 ξ it Cog i ξ it T eh i ξ it dt emp it ξ it Si n n ξ it 2014 t Standard errors are auated through bok bootstrap. Optimisation is arried out through the Neder-Mead agorithm and to ensure onvergene dierent starting points were tried. Finay, I reover TFP estimates as foowing: ω it = ed it α k it α it x it β (10 20

21 6 Resuts In tabe 2, I present the estimates of our singe output prodution funtion mode aong with the ordinary east square (OLS and the xed eet (FE estimators whih are respetivey presented in oumn 1 and 2 as touhstones of our mode. The point estimates are assoiated with bootstrapped standard errors in parenthesis. First, I onsider the estimates of the inputs' eastiities α j with j = k,, and it is immediatey evident as estimates of these paramers dier signianty aross mhods. In partiuar, a omparison bween OLS and the FE mode, enightens how using ony the rossetiona variation to identify input eastiities impies not aounting for produtivity dierenes amongst DH rm. Treating the same DH rm aross time as severa dierent observed units greaty biases the resuts sine more produtive rms are ikey to use more quantity of the inputs. This indues to strengthen (weaken inreasing (dereasing rurn to sae. On the other hand, FE estimator expoits ony the year-to-year variation in DH rms' inputs: estimation by FE aounts for dierenes aross DH rms, but these dierenes remain onstant over time. I observe dereasing rurn to sae as expeted from tehnia iterature on DH pants, see rã nnund and Kristrà m (1999, even after ontroing for size dummies 6. Moreover, estimated oeients are onsistent with previous estimation of apita and abor's margina produtivity in a vaued added prodution funtion ontext, see for referene the ited artie of rã nnund and Kristrà m (1999. I nd that simutaneity bias aets upward oeients of apita. A apita's oeient, equa to0.344, is in ine with a apita intensive industry ike DH rm. This is aso in ine with our hypothesis of restrained substitution bween apita and therma energy. I move to the main fous of this paper, the eets of the apita quaity and PPPs. In ine with the theoria framework, I nd a non signiant margina eet of our proxy for tota quaity investment in buiding's design, whih ontros for the apita quaity a i. I report a signiant positive eet of the PPP dummy of 0.128, whih in eve terms orresponds to a 14% inrease in output. I nd a strong and highy signiant margina eet on output of a quaity investment in buiding's design for PPP rms, the interation term. In partiuar, reduing by one unit (negative the ength of pipeine every 10 2 m 3, shifts up the expeted hange in og of output by for PPP rms. In eve terms, it orresponds to an output inrease of 15%. Amongst the ontro variabes, the ogeneration dummy is strongy signiant and positive, suggesting that the ontemporaneous prodution of eetriity and therma energy 6 Dereasing rurn to sae are not in ontrast with a natura monopoy with U-shaped ost funtion. 21

22 aets the heat distribution therma apabiity of DH rms. I nd a strong signiant positive eets, respetivey equa to and 0.783, of the geographia dummies. A dummy for the 2014's hot winter is negative and strongy signiant. Dierenes in average extrated have no meaningfu eet on the therma energy distribution. 7 Robustness hek 7.1 Aternative Approah As a rst robustness hek, I propose the Woodridge (2009 estimator. This estimator is robust to the ritiism of Akerberg a. (2015 and an be onstruted reying on either intermediate materias or investment to proxy for produtivity. The iterature refers to the former as the WoodridgeLP and the atter as the WoodridgeOP. The Woodridge (2009 onsists of a two-equation system GMM estimator, where ontemporaneousy the rst aounts for the dynami proess of produtivity and the seond direty approximate the unobserved tehnia eieny term. The Markov proess of tehnia eieny and ω it are both obtained by the approximation of two unknown funtions, g(. and h(.. This estimator expoits moments on the vetor error term : E [ ξ it ɛ it I it where I it is the usua information s of a DH rm i at t. This approah avoids bootstrapping to obtain standard errors on the prodution funtion oeients sine the two equations are jointy estimated in a singe step. However, this proedure requires jointy estimation of a poynomia oeients that approximate the unknown funtions g(. and h(., togher with a prodution oeients and the ontro variabes. This means that you need a searh over a arger paramer spae than ACF mhodoogy sine you have to searh jointy for the prodution funtion oeients, the ontro variabes oeients, and a poynomia oeients. In tabe 6, I report the estimates. In the rst oumn, I used the intermediate materia as proxy. The eastiities estimates do not dier signianty from the two stages mode. Fousing on the PPP eet, the interation term β int has a positive and signiant eet of 0.139, onsistent with the baseine mode estimates. A unit inrease in apita quaity inreases the output in eve terms by 15%. The PPP dummy resuts positive, but not signiant. A shift in the status of pant inreases output by 17%. In oumn 2, I used the yeary variation in pipeine's ength as a measure of investment. Using investment greaty aets the dimension of the sampe, due to the presene of many ] = 0 22