The Simple Economics of White Elephants

Transcription

1 The Simple Eonomis of White Elephants Juan-José Ganuza Universitat Pompeu Fabra and Barelona GSE Gerard Llobet CEMFI and CEPR May 16, 2016 Abstrat This paper disusses how the design of onession ontrats affets the inentives for onessionaires to aquire information about the future profitability of the projet. We show that the onession model itself is not ondutive to this aquisition of information. As a result, ontrators have inentives to arry out projets that if they had information they would not undertake beause they have a negative net present value, but that in expeted terms they might still find profitable. This lak of inentives for firms to aquire information gives raise to white elephants. We show that our results are preserved in the ase of ompetition and we study a variation of the flexible-term ontrat that aounts for this information aquisition problem. JEL odes: D82, D86, H21, L51. keywords: Conession ontrats, information aquisition, flexible-term onessions. We benefited from omments by Ginés de Rus and audienes at Universitat de Barelona, Universidad de Las Palmas, and University of Toronto. Comments should be sent to juanjo.ganuza@upf.edu and llobet@emfi.es. 1

2 1 Introdution On May 28, 1873 the New York Times published an artile alled White Elephants that starts with the following paragraph When a Siamese despot takes a grudge against one of his poorer subjets, and determines on his ruin, he does not ut off the delinquent s head and onfisate his property. On the ontrary, he makes him a present he sends him the handsomest and healthiest white elephant he an find. The lukless reipient knows at one that his fate is sealed. He knows that the beast will eat him out of house and home without the possibility, on his part, of resistane. He annot sell or give away the fatal gift, for no one would aept it, and the attempt to get rid of it even would be diret treason and sarilege. He sits down with Oriental resignation to submit to the inevitable, and the white elephant devours his substane. As Bullen (2011) explains, this story is probably a myth, as white elephants were onsidered a symbol of virtue and status in Siam and no king would onsider them burdensome. Nevertheless, this story has taken root in the eonomis literature, popularized in papers suh as Robinson and Torvik (2005), and is now used to identify failities and infrastrutures of little pratial use or value. More preisely, white elephants are assoiated with projets with a negative soial value. The pereption that these white elephants are ommon is widespread and eah ountry has its favorite example: The Montréal-Mirabel International Airport was one the largest in the world in terms of surfae; 1 the New South China Mall, the largest mall in the world, 1 Designed for 50 million passengers a year when it opened in 1975 it never handled more than 2.8 million. See Krauss, C. End of Era Near in Montreal for White-Elephant Airport, Ot 3,

3 has sat mostly vaant; the Brisbane s Clem Jones Tunnel had less than 50% of the projeted traffi even after tolls were slashed by half; the Radial Highways around Madrid suffered from an even superior demand overestimation. 2 In this paper we disuss how these white elephants may ome about in the onstrution of publi infrastruture by private firms, whih are ompensated through onession ontrats. We argue that standard prourement proedures do not provide inentives for firms to get informed about relevant harateristis of the demand (or the ost) and, as a result, ontrators engage in insuffiient sreening of projets and end up building infrastrutures that are unneessary. Conession ontrats, typially between a government ageny and a private onsortium of firms (the onessionaire), involve the transfer of the onstrution and/or the operation of an asset from the former to the latter for a period of time. Toll highways are a lassial example. Their onstrution is managed by a onessionaire who engages in a long-term ontrat with the government designed to reover the large investment ost through user fees (i.e. toll revenues). This kind of shemes has been extended in reent years to all types of Publi-Private Partnerships (PPPs). 3 They are now ommon in the onstrution of roads, prisons, airports, hospitals, railway infrastruture, et., where the government pays a fee aording to their usage. As opposed to what ours in publi-work ontrats where the government assumes all risk and manages the infrastruture diretly, onession ontrats are used to transfer the risk to the onessionaire. The risk of suh a projet is high, sine the PPP onessions overing these infrastrutures 2 Aording to Engel et al. (2015) first year traffi of the R-2, R-3, R-4 R-5, M-12, and AP-41 highways was between 56% and 82% lower than antiipated. 3 See Engel et al. (2014) for an overview of the rise of the investment in infrastrutures finaned through PPPs. They report that in Europe they went from irrelevant in 1990 to a lose to e 30 billion industry in In low and middle-inome ountries PPP invesment reahed US$160 billion in

4 are long-term ontrats to allow investors to reover the huge upfront investment, and their profitability depends on variables (traffi, osts, et.) that are diffiult to foreast in a long horizon. In the ase of demand estimation, Bain and Polakovi (2005) report, using a sample of highway onession projets olleted by Standard and Poors (S&P), that first-year traffi volumes averaged about 76% of their predited values and the error had a standard deviation of A similar error persisted in the years 2 to 5. Flyvbjerg et al. (2005) analyzes 214 road projets in 14 ountries mainly free roads, and although they find almost no overestimation bias, the foreasting errors are even larger than in the previous ase (a standard deviation 0.44). 4 It is worth to notie that the private onession projets analyzed by S&P exhibit larger demand overestimation than the publi-work projets studied by Flyvbjerg et al. (2005). This is partiularly striking sine one of the main advantages of the onession model over a standard publi-work ontrat is preisely the fat that a firm an better assess the demand sine its own money is at stake. Our paper provides an explanation for this result that arises from the interation between the (asymmetri) onsequenes of the unpreditability of revenue (or osts 5 ) and the inentives for firms to aquire information. Regarding the revenue risk, it is often the ase that if traffi is lower than expeted, onessionaires will fore a renegotiation. Guash (2004) analyzes onession ontrats in Latin Ameria and shows that over 30% of onession ontrats are renegotiated. In the transportation setor this proportion reahes 54.7%. The results are similar in other onessions haraterized by huge sunk investments, long onession terms and demands risk suh as water and sanitation, where renegotiation ours in 74.4% of the ases. Importantly, Guash (2004) also reports that most of the renegotiations 4 Interestingly, Flyvbjerg et al. (2005) also show that railway demand is systematially overestimated worldwide. 5 Flyvbjerg et al. (2003) analyze a sample of 258 infrastruture projets aross 20 ountries and 5 ontinents, and found that 90% of these projets were subjet to ost overruns. 4

5 favor the onessionaire by raising tariffs (62% of the ases) and/or through a derease in the required investment. In other ases the duration of the onession is extended. These hanges are in ontrast with what ours when revenues are higher than expeted. In that ase onessionaires typially ash the extra profits. These asymmetries are ontroversial and, in many ountries, they have had an impat in the publi debate. In this paper we highlight another important distortion that these asymmetries might entail. The ore idea of our work is that if the potential losses of the onessions are limited by a future renegotiation (while the firm appropriates the upside) the inentives to aquire information are redued, negatively affeting projet seletion. This mehanism is onsistent with the puzzling evidene disussed above indiating that demand overestimation is more prevalent in onession ontrats ompared to publi-work projets. We propose a prinipal-agent model where the publi setor (the prinipal) is the sponsor interested in arrying out a publi-work projet. This projet has an unknown value that might be unovered with the ostly aquisition of information by the ontrator (the agent). The prinipal designs a simple onession ontrat that assigns a proportion of the value of the projet to the ontrator, for example, through the toll revenues arising from a limited duration of the onession. The agent deides on the aquisition of information and ontingent on that whether to invest in the projet or not. The goal of the prinipal is to foster the aquisition of information and to indue investment only when the value of the projet is higher than the ost, avoiding white elephants. We haraterize the optimal onession ontrat and we show that both objetives (undertaking only projets that generate positive surplus and induing the aquisition of information when it is effiient to do so) annot be attained at the same time. As a result some white elephants inevitably emerge in equilibrium. The intuition is as follows. Suppose 5

6 first that the ost of aquiring information is small. Then, the first best an be attained by designing a onession ontrat that alloates the share of the revenue to the firm that, one informed, allows it to break even only when a projet has a positive soial value. Naturally, the inentives to aquire information derease as the ost of this information inreases. To prevent the firm from arrying out the projet without information the onession ontrat must be distorted. In partiular, the value of information raises if the share of the revenues that the firm appropriates is redued and avoiding bad projets beomes more valuable. In this seond-best world, some good projets are not undertaken. Furthermore, for a suffiiently high ost of information, the aquisition of information that ours in the first best is too expensive, in terms of inentives, to spur in the seond best. In that ase the prinipal prefers not to indue the aquisition of information, leading to some bad projets (white elephants) to be undertaken in equilibrium. Our result is not speifi to the ase studied here and we show that similar impliations arise when we extend the model to allow for ompetition. In pratie, as mentioned above, an important element of these onession ontrats is the limit on the losses that the ontrator an inur due to the renegotiation or the resue of the infrastruture by the publi setor. 6 When we introdue this element in the model we show that the lower are the losses that the firm might absorb the more ritial is the problem of providing inentives for the firm to aquire information. As a result, distortions inrease leading to more white elephants. All our analysis relies on the assumption that the firm an aquire information beyond 6 In ountries like Spain, there exists an expliit legal mehanism, denoted as Responsabilidad Patrimonial de la Administration, for whih an underwater onession is taken over by the state and the firm is ompensated aording to the investment arried out. In line with the poliy reommendation of this paper, a reent hange in the law has linked this ompensation to the present value of the ash-flows of the onession at the time of the resue. 6

7 the knowledge of the prinipal. This assumption is very reasonable in the ase of many PPPs in whih the ontrator might have an expertise in a partiular setor or a partiular market. We laim, however, that this assumption is also appealing in a more general ontext even when the firm does not neessarily have an advantage in the aquisition of information simply beause the publi setor typially disloses all the available information prior to the ontrat. There are many reasons why this ours. There are legal obligations to dislose all relevant information for the projet. Furthermore, the provision of information might entail effiieny gains by induing a better math between the firm and the projet and by reduing the winner s ourse when the projet is alloated through an aution. Thus, our information aquisition proess ought to be understood as the additional preision in the assessment of the value of the projet that the firm might obtain by arrying out its own study. Our paper is related to the literature that has studied the optimal onession ontrats. The prevalene of the renegotiation highlights the importane of managing the risk of these long-term ontrats. While the firm has ontrol of most ost omponents, often the demand is exogenous to its ations. This might be due to many reasons suh as the fat that the quality of infrastrutures like highways an be speified as part of the ontrat. As a result, the general priniple in inentive ontrats, that the firm should be subjet to the risk that an be affeted by its own ations, implies that demand risk should be absorbed by the government. One way to ahieve this goal is to adjust the duration of the onession to the evolution of the demand. Engel et al. (1997, 2001) proposed the Least Present Value of the Revenues (LPVR) mehanism that has beome the most influential way to exploit this idea. The mehanism onsists on a flexible-term onession that awards the ontrat to the bidder that demands the lowest disounted total revenue for the projet. The winner is then entitled to 7

8 reeive the revenues of the onession up to the point in whih their disounted flow equals the present value revenue offered in the bid. At that point the onession expires. The previous literature has usually ignored the optimal seletion of projets whih is the main fous of our work. Here we show that although in our model the revenues of the projet are exogenous, a standard appliation of the LPVR mehanism is suboptimal beause it does not provide inentives for firms to aquire information. Taking this effet into aount requires some demand risk to be transferred to the ontrator in order to provide inentives to get informed. 7 The LPVR mehanism ontains, however, the powerful idea that it is optimal to enrih the onession ontrat with the available information about the realized demand. In one of the final setions of the paper we take up on this idea and we allow the onession ontrat to be onditional on the realized demand. In that ase, we show that a flexible-term onession ontrat in the spirit of the LPVR emerges as optimal and ahieves the first best. As in the standard appliation, when the realization of the demand is suffiiently high (indiating that it is likely that information was aquired), the firm is ompensated for the total ost. It also reeives a ompensation when the projet is not arried out. If demand is low, however, the firm is penalized. In spite of the pratial limitations of this mehanism we believe that this approah opens a new way to think about the provision of inentives in onession ontrats when projet seletion matters. We also haraterize the optimal ontrat when this ompensation is not possible and we show that the distortions that arise are similar to those that we desribed in the benhmark model. The paper proeeds as follows. Setion 2 and 3 disuss the basi model. Setion 4 introdues limited losses. Setion 5 disusses the effets of ompetition and setion 6 haraterizes 7 This is beause the expeted realization of the demand is different depending on whether the ontrator is informed or not. So, in some sense, the demand is not ompletely exogenous to the ations taken by the ontrator. 8

9 the optimal flexible-term onession ontrat. Setion 7 onludes. All proofs are relegated to a tehnial appendix. 2 The Model A government onsiders the possibility of undertaking a projet of a know ost of > 0. Together with the onstrution ost the government must aount for the opportunity ost of the projet d > 0. This opportunity ost might be interpreted as the benefits of an alternative projet that ould be funded with the same resoures or, in the ase of a publi work projet, the alternative uses that resoures devoted to it, for example land, may have had. The projet is not arried out diretly by the government but by a private firm, that we denote the ontrator. 8 The return of the projet is unertain. It produes a total value θ drawn from a distribution G(θ) in the interval [0, 1] with density g(θ), assumed to be positive in all the support. The value the projet an be assessed before onstrution takes plae if an amount k 0 is invested in a study. For simpliity, we assume that if this ost is inurred the exat value of θ is revealed. Otherwise, the value is only revealed after investment takes plae. Throughout the paper we make the assumption that even without information it is in the interest of soiety in expeted terms that the projet is arried out. That is, E(θ) = 1 0 θg(θ)dθ > + d. (1) Thus, the main effet of aquiring information is to redue the proportion of projets that are undertaken by weeding out those that are known to have a low value. It is natural to 8 The onession of an infrastruture distinguishes between the firm that builds it, the ontrator, and the firm that manages it, the onessionaire. For the purpose of this paper this distintion is irrelevant, and we all the firm simply as the ontrator. 9

10 assume that projets have an ex-ante positive soial value sine we are in a ontratual stage. Beyond this assumption our results are distribution free. In exhange for inurring in a onstrution ost the ontrator reeives a ompensation onsisting of a proportion β [0, 1] of the returns from the projet, awarded by the prinipal. This is typially the ase, for example, in infrastrutures like toll highways. In that ase, we an interpret θ as the total traffi generated and β as how many years the ontrator will be able to ollet tolls from it. 9 Furthermore, we also assume that the investment in obtaining information an only be arried out by the ontrator. An interpretation of this assumption is that the government has already olleted information whih has been made publi and it is already embedded in the distribution G(θ). The firm an invest in obtaining a more aurate signal. Importantly, we will assume that whether the firm has inurred in the ost of information k or not is not ontratible. The government s objetive funtion is to maximize soial welfare. As we will see next, attaining this aim implies minimizing deision errors: reduing the possibility that projets with a low value of θ are arried out while, at the same time, not passing over soially profitable investment possibilities. When several ontrats lead to the same soial welfare we will assume that the government hooses the one that minimizes firm profits. Before we haraterize the optimal ontrat we briefly disuss the first best. This alloation will beome useful as a benhmark in the rest of the paper. 9 In this paper we abstrat from other important dimensions, like the amount of the toll, whih affets how muh of the ost is reovered eah period, and an be ompensated with the duration of the onession. This is not a new trade-off and it has been studied in other ontext like in the ase of patents, starting with lassial works like Nordhaus (1969). Weyl and Tirole (2012) study how pries an also be used in order to sreen private information in suh a ontext. 10

11 2.1 The First Best If no information is aquired our previous assumption, in (1), implies that the expeted value of a projet of unknown return θ is higher than + d and it should be arried out. Thus, information should be aquired if it produes higher soial welfare. The investment of an amount k unovers the return of the projet and it allows to arry out only those for with θ θ. Aquiring information will be effiient if max θ 1 [θ ( + d)] g(θ)dθ k 1 θ 0 θg(θ)dθ ( + d), leading to an optimal threshold in the value of the projet of θ s = + d. Hene, information should be aquired if θ s k K s [θ ( + d)] g(θ)dθ, 0 In other words, if k K s information is gathered and a bad projet is avoided. Instead, if k > K s, it is soially optimal not to aquire information and the projet should be arried out. 3 The Optimal Contrat In order to illustrate our analysis it is useful to start by pointing out that if information ould be aquired by the firm at no ost the first best ould be easily implemented. We know that the ontrator would always aquire information and it would only arry out those projets that produed a positive return, identified as βθ. As a result, the first best in terms of the seletion of the projet an only be attained by hoosing β = < 1. +d The intuition is straightforward. Sine the firm does not internalize the opportunity ost of the investment, d, the duration of the onession must be redued in order to eliminate the exessive inentives to invest. 11

12 When k inreases the ontrator s deision to get informed will depend on whether the losses avoided by using this information are greater than k or not. That is, the ontrator will get informed if max θ 1 [βθ ] g(θ)dθ k 1 θ 0 βθg(θ)dθ. This problem yields a profit-maximizing threshold θ = β under whih the ontrator will deide to get informed if β k K(β) [βθ ] g(θ)dθ. 0 Notie that the ritial value K(β) is dereasing in β, K β (β) = θg(θ)dθ < 0. 0 Intuitively, a higher β implies a larger set of projet realizations that are profitable for the firm whih in turn implies that the inentives to get informed are redued. As a result, when k > K ( +d) a onflit arises. Providing inentives to invest in suh a ase requires hoosing β < +d and this derease in profits disourages the firm, one informed, to arry out some profitable projets. The next lemma summarizes this disussion. Lemma 1. For values of k [ K ( +d), K s ) the first best annot be attained. This result implies that the first best alloation will be possible in two irumstanes. First, when k is small the firm has inentives to get informed and, thus, β maximizes soial welfare. Seond, when k is suffiiently high so that gathering information is not soially optimal there is no inentive problem and it is enough that β allows the firm to break even in expeted terms for the projets to be undertaken. In the remaining situations, when the first best annot be attained, the government trades off two types of distortions. On the one hand, it an give up the inentives for the firm to 12

13 learn so that bad projets are arried out. On the other, it an distort β in order to provide inentives for the ontrator to learn but, as a result, forestall some good projets. These two distortions will give raise to standard Type-I and Type-II errors. Type-I errors arise beause in order to entie the ontrator to invest, the value of β must be distorted downwards. The lower is β the higher is K(β). That is, the inentives to get informed inrease sine the losses the ontrator suffers when θ is low and the projet has been arried out beause no information was gathered are higher. Of ourse, this distortion implies that a range of projets with a value of θ higher that + d will not be undertaken sine β is too low. Thus, the optimal β is the highest value that provides inentives for the ontrator to get informed, β(k) = K 1 (k). The ost of these Type-I errors for a given k is E I (k) = β(k) +d (θ ( + d))g(θ)dθ. Following the previous disussion, Type-I errors arise beause projets with θ [ + d, ] β(k) have a value greater than + d but will not be arried out if the firm gets informed. Of ourse, the size of this error is inreasing in k, sine the higher is this ost the higher will need to be the distortion in β to entie learning. Type-II errors arise in those ases in whih the sponsor deides not to provide inentives to learn the value of the projet. Consequently all projets are arried out implying a soial ost of +d E II = (θ ( + d))g(θ)dθ = K s, 0 that must be ompared with the savings that soiety arues when k is not inurred. The optimal ontrat is haraterized by omparing Type-I and Type-II error osts. 13

14 Proposition 1. The optimal ontrat orresponds to where β +d (k) = β(k) E(θ) if k < K ( +d), if K ( +d) < k < K, otherwise, E I ( K) + K = E II. Notie that sine E II = K s, K K s. Figure 1 illustrates how the optimal value of β hanges when k varies together with the lowest value of the projet that will be implemented, θ. As Lemma 1 showed, the optimal ontrat orresponds to the first best when k is very low or very high, k K ( +d) or k K s. We have two regions in-between. When K ( +d) < k < K the firm will invest beause the lower Type-I error dominates. Instead, [ when k K, K s] it is not optimal to provide inentives for the ontrator to get informed. The Type-II error beomes less ostly. The projets that are arried out in this region, beause the firm does not have inentives to aquire information although it is soially optimal to do so, will be identified as white elephants. 4 Limited Losses In the basi model the ontrator invests in the projet or + k depending on whether information is aquired or not. This investment sets a ap on the maximum losses that the firm might suffer due to limited liability. In many ases, however, the government imposes additional limits on the losses that the ontrator might bear. In ountries like Spain the prourement of publi projets has traditionally inluded an amount that the government will over in ase some unexpeted osts arise or if the demand turns out to be lower than antiipated. More generally, the prospets of a ostly and unertain renegotiation proess 14

15 β +d β(k) E(θ) K ( ) +d K K s k θ + d K ( ) +d K K s k Figure 1: Seond best as a funtion of k. might motivate governments to subsidize underwater onessions. We denote the maximum losses that the firm may inur as L and we restrit them to be between 0 and. The analysis in this ase is very similar to the one we onduted in setion 3. Beause now the losses are apped by L, profits will be L for any realization θ < L. As a result β we obtain that information is aquired if max θ 1 θ [βθ ] g(θ)dθ k 1 L β ( L [βθ ] g(θ)dθ LG β Notie that when the firm gets informed, losses will never be inurred and as a result L does not play a role. The previous expression yields a new threshold ost of information that provides inentives for the ontrator to get informed and that, with some abuse of notation, we denote as K(β, L). When L = we obtain the same threshold as in the baseline model, K(β). At the other extreme, when L = 0, the threshold is equal to 0. In this last ase, the ). 15

16 ontrator will never get informed beause the value of information is preisely to eliminate those realization of θ for whih the firm makes losses and this is something that L = 0 already guarantees at no ost to the ontrator. errors. The optimal ontrat an again be ast in terms of the omparison of Type-I and Type-II Proposition 2. The optimal ontrat under limited losses orresponds to if k < K (, L), β +d +d (k, L) = β(k, L) if K ( +d, L) < k < K(L), otherwise, where E(θ) E I ( K, L) + K = E II, (2) The struture of the optimal ontrat bears many similarities with the one in the benhmark ase. When k is low the first best an be implemented but, ompared to the benhmark ase, the threshold value will be lower, sine K ( +d, L) inreases with L. For intermediate values of k, the sponsor prefers to indue learning by distorting β downwards. As in the benhmark ase, for a given k, it is optimal to hoose the highest value of β that satisfies the ondition for learning, β(k, L). In other words, k = K( β, L). Beause the only distortion is that some good projets are not arried out, only Type-I errors an arise and their ost an be omputed as whih is dereasing in L. E I (k, L) = β(k,l) +d (θ ( + d))g(θ)dθ, For higher values of k it is not optimal for the sponsor to indue learning at all and, thus, only Type-II errors an arise. These errors are idential to the ones in the benhmark ase and, in partiular, they do not depend on L whih, from a soial point of view, is just a transfer to the firm. 16

17 β +d β(k) E(θ) K ( K (, L), ) +d +d K(L, ) K K s k θ + d K ( K (, L), ) +d K K s +d K(L, ) k Figure 2: The effet of the limit in losses. The dashed line orresponds to L < whereas the solid line indiates the benhmark ase L =. The minimum value of k for whih it is not optimal to indue learning orresponds to the one for whih the ost of the Type-I error plus the ost of learning equates the ost of the Type-II error, as indiated in (2). Notie, though, that sine E I is dereasing in L we have that the ritial value K is inreasing in L. That is, when the ontrator an absorb fewer losses the soial value of fostering information aquisition is redued and the threshold value for whih it is optimal that the firm arries out all projets dereases. This effet implies that the white elephants are more likely when L is lower. Figure 2 also shows that β is dereasing in L. All this disussion an be summarized in the following result. Corollary 1. When L inreases, 1. Soial welfare inreases, 17

18 2. White elephants are less likely, and 3. Equilibrium deision errors are smaller. As it transpires from the previous analysis, institutional reforms aiming to inrease L will raise soial surplus. This ours, for example, in the ase of renegotiation of an underwater onession (a situation when future revenues are not enough to repay the remaining debt). Our results indiate that if the ontrator expets to reeive more than the present value of the future ash-flows of the onession the ex-ante inentives to aquire information will be harmed. A ommitment to prevent that ould be aquired if the government speified that in ase of bankrupty the onession would be taken over and autioned off again. The reeipts from this aution would go to ompensate the previous onessionaire. From the previous disussion we an also onlude that enlarging the spae of ontrats that an be offered to the ontrator by inluding a subsidy T 0 will have a similar effet as limited liability. When it is optimal to arry out the projet the firm reeives the subsidy regardless of whether information has been aquired or not. Instead, if θ is low the subsidy is paid only when the projet is arried out anyway, dereasing the payoffs from aquiring information. Proposition 3. Suppose that the prinipal offers a onession with duration β together with a subsidy T 0. Among all the ontrat ombinations that lead to a threshold θ above whih the projets are arried out, the inentives to aquire information are maximized when T = 0. As we will see later, however, the previous result may hange when the subsidy might be a funtion of θ. In that ase, a higher subsidy an be assoiated to a higher traffi realization and, as a result, be used to provide inentives and ompensate the osts of the aquisition of information. 18

19 5 Competition Our benhmark model assumes that only one firm an arry out the projet. However, most onessions are awarded ompetitively through an aution. Along those lines, in this setion we disuss a simple model of ompetition that emphasizes an additional fore that operates in the same diretion and omplements the results disussed in our benhmark framework. Consider the ase of two idential firms i = 1, 2 bidding to build the same projet. The projet is alloated aording to a seond-prie aution. Eah firm bids β i. The firm that offers the lowest β wins the aution and the prie, denoted as β, is set aording to the losing bid. As in the previous setion this prie an be interpreted as the proportion of the value of the projet that it is alloated to the ontrator, for example, through the ombination of the toll level and the duration of a onession ontrat. Hene, the firm that ommits to reeive the lowest proportion of the value of the projet wins. In the benhmark model the prinipal sets β optimally. An important differene here is that β is now determined in equilibrium and not diretly as part of the ontrat. However, as it is typially the ase in the design of autions, the prinipal an still affet the resulting β by setting a reserve prie. In partiular, we denote this prie eiling for whih the bid will be aepted and the onession awarded to the winning firm as β. Similarly to what we assumed in the benhmark model here we assume that firms deide to get informed or not before plaing a bid and after knowing the reserve prie in the aution. To keep things simple, we also assume that, although the result of this investment is private information, whether a firm gets informed or not is known to the other firm before plaing this bid. The timing of the model is as follows. In the first stage, the government sets the reserve 19

20 prie. Seond, firms deide simultaneously whether to pay k to get informed or not. Finally, firms deide simultaneously on β i. Solving the model by bakward indution, we start by analyzing the bidding behavior of firms in the last stage as a funtion of their information investment deisions. As it is standard, we fous on the weakly dominant strategy equilibrium of the seond-prie aution. In our framework this means that firm i bids a value β i suh that this share of projet allows it to break even given the available information. Of ourse, if this break-even β i is higher than β firm i will not partiipate in the aution. There are three ases to be analyzed. First, assume that both firms get informed. Then, eah firm learns the real θ and bids β i =. As a result, their profits are equal to k. θ Seond, none of the firms might get informed. In that ase, eah firm will bid aording to the expeted value, β i = /E(θ) as long as β > /E(θ) and it will not partiipate otherwise. In either ase, firms will make expeted profits of 0. Finally, if one firm gets informed, say firm 1, firm 2 will not partiipate due to the Winner s Course. As firm 1 knows the profitability of the projet and bids a break-even β 1 = /θ, firm 2 faes two outomes. Either it loses the aution and gets 0 or it wins and in that ase, it loses money. Thus, it is a weakly dominant strategy not to partiipate and, onsequently, the equilibrium prie is given by the reserve prie β. In this ase we an ompute expeted profits for firm 1 when it gets informed as π ( β) = 1 β ( βθ )g(θ)dθ k. With the previous payoffs, we an now move to the seond stage of the game in whih firms deide whether to get informed or not. In the next payoff matrix we represent the profits of both firms as a result of their investment deision. 20

21 Firm 2 Investment No Investment Investment Firm 1 k, k π ( β), 0 No Investment 0, π ( β) 0, 0 Notie that if k is suffiiently large π ( β) 0 and the only equilibrium orresponds to neither firm gets informed. Otherwise, if π ( β) > 0, the payoffs resemble those of a Chiken Game. As a result, this game has two asymmetri equilibria in pure strategies and one symmetri mixed-strategy equilibria. We will fous on the latter, in whih firms randomize between getting informed (with probability α i ) and not doing so. This equilibrium an be easily haraterized by equating the payoff of aquiring information with those that arise when the firm does not get informed, 0. In the symmetri equilibrium α i = α for i = 1, 2 and equal to (1 α ) 1 β ( βθ )g(θ)dθ k = 0. (3) In the first stage the prinipal sets the reserve prie, β to maximize welfare. Notie that this reserve prie only affets the probability that firms get informed. From equation (3), we an observe that inreases in β raise α. This is an important differene with respet to our benhmark model. In that ase, hanges in β affeted the rents that firms obtained when they deided not to get informed. Here these rents are always 0 by virtue of ompetition. We an write down the maximization problem of the prinipal as max β 1 β β (θ ( + d))g(θ)dθ + (1 α ) 2 (θ ( + d))g(θ)dθ 2α k, s.t. (1 α ) 1 β 0 ( βθ )g(θ)dθ k = 0. 21

22 0.5 1 β 0.45 α k k Figure 3: Optimal reservation prie and probability that the eah firm aquires information as a funtion of k. The remaining parameters are = d = 0.2 and θ U[0, 1]. The first term refers to the surplus of the projets that generate non-negative profits for a firm when it is informed. Those projets are always undertaken regardless of whether any firm is informed or not. The seond term refers to the projets than informed firms would not arry out given the reserve prie. Those projets are undertaken when both firms are uninformed, whih happens with probability (1 α ) 2. The third term aptures the total expeted osts of firms getting informed. This maximization has no expliit solution and for this reason we rely on the simulation in Figure 3 to onvey the intuition for the results. When k = 0 firms always get informed and α = 1. In that ase, it is soially optimal to hoose β = effiient projets and only them are arried out. +d as this guarantees that all As in the benhmark model, when the osts of learning inrease the prinipal must derease β in order to provide inentives for firms to get informed. As notied before, however, the reason is different. Competition leads to exessive inentives for firms to get informed. This is the result of a standard externality: firms aquire information without taking into aount that by doing so they redue the value of the information that their 22

23 ompetitor is also aquiring. As k beomes suffiiently large, it is optimal to indue no learning. This is ahieved through β dissipate all the profits.. In that ase, ompetition among firms will E(θ) The benhmark model and the ompetition setup studied here onstitute two extreme ases in whih inreases in the ost of aquiring information lead to a derease in the share of the projet being assigned to the ontrator, although for very different reasons. In a more general ase several heterogeneous firms might partiipate in the aution for example, with different osts i, leading to an intermediate level of ompetition. Our results for the extreme ases makes intuitive the predition that both effets would emerge in ombination in this situation, although in a weaker version. 6 Flexible-Term Conession Contrats The optimal ontrat haraterized in the previous setions assumed that k was not ontratible but also that the ontrat offered, following standard pratie in onessions, ould not be a funtion of θ. In reent years, however, it has been argued that many of the distortions would be mitigated if the ontrat would depend on the realized return of the projet. Engel et al. (2001) have onviningly argued that in infrastrutures suh as highways the duration of the onession should depend on their traffi. Highways busier than expeted should be subjet to a lower onession period, enough for the ontrator to reover the investment osts. Highways that are less suessful than expeted should see the duration of the onession extended as muh as neessary until the firm broke even. In our benhmark model this kind of ontrats an be easily aommodated by assuming that β(θ). Notie, though, that the flexible-term onession in this ase must ompensate not only for the osts of building the infrastruture but also for the ost of aquiring information. 23

24 For that reason, we interpret the flexible-term onession as a ontrat in whih the firm reeives a value of β { β ft (θ) = min 1, + ρ }. θ As in the benhmark model, β = 1 an be interpreted as a onession of infinite length. In this speifiation the duration of the onession inludes, besides the ost of building the infrastruture, an additional omponent that we denote as ρ, whih orresponds to the extra payment that the firm must reeive for gathering information. If the ontrator aquires information profits orrespond to 1 (β ft (θ)θ )g(θ)dθ k = ρ(1 G( + ρ)) + +ρ (θ )g(θ)dθ k. This seond expression an be interpreted as follows. For any θ + ρ, β ft (θ) is set so that the firm makes profits from the onession equal to ρ. When θ < +ρ and the highest possible return from investment never exeeds ρ the onession is extended to infinity, β(θ) = 1. Nevertheless, one information is aquired and k is sunk it is in the interested of the firm to arry out any projet θ. The profits for the ontrator if it deides not to get informed an be written in a similar way, +ρ 0 (θ )g(θ)dθ + ρ(1 G( + ρ)). The main differene here is that without information all projets are arried out even those with θ < but the ost of information is spared. The omparison of both alternatives implies that the ontrator gets informed under a flexible-term ontrat as long as k 0 (θ )g(θ)dθ = K(1) < K s. 24

25 As a result, two distortions arise. If k < K(1) the ontrator gets informed but it undertakes projets with a value θ [, + d) whih are ineffiient. 10 If k [K(1), K s ] the firm does not get informed and undertakes the projet regardless of its value. That is, white elephants also arise in equilibrium under this ontrat. Standard flexible-term ontrats are, therefore, ineffiient in terms of providing inentives for firms to get informed. The reason is that this mehanism is effetive both in limiting the profits that the firm an obtain when the realization of θ is large and at the same time ompensating the firm with an inreased duration in those ases in whih θ is low. As our disussion illustrates, however, by shifting the risk from the firm to the government, the mehanism also dereases the inentives for the firm to beome informed in the first plae. In some sense, it operates as a demand-ontingent limit in the losses and suffers from problems similar to those disussed in previous setions. The previous Flexible-Term Contrat an be improved upon when the proportion of the value of the projet awarded to the ontrator an be made a funtion of the observed value of the projet in a more general way and, probably more importantly, if the prinipal may ompensate the firm for not undertaking some projets. Proposition 4. A Flexible-Term Contrat with payments when the projet is not arried out an implement the first best for any value of k. This ontrat an be haraterized as: If k K s and θ + d then β (θ) = +ρ P (k) θ ; θ < +d then β (θ) = 0 if the projet is undertaken and otherwise the firm obtains a ompensation ρ N (k), 10 For this argument we assume that ρ is suffiiently high so that the ontrator obtains non-negative expeted profits if it aquires information. Otherwise, information would never be aquired. 25

26 where { } k ρ N (k) = max G( + d), 0, ρ P (k) =ρ N (k) + k 1 G( + d). If k > K s then β =. E(θ) When k K s the previous ontrat is omposed of three different elements. In the spirit of other flexible-term ontrats, β (θ) is suh that when the projet is soially valuable the firm obtains the same ompensation regardless of θ. This ompensation is higher than the ost and equal to ρ P (k) k, whih in expeted terms overs the ost of information. When the projet has a low value, however, the firm is awarded a onession with β = 0 as this is an indiation that no information was aquired. Finally, the optimal ontrat also requires a ompensation when the ontrator deides not to arry out the projet, ρ N (k). The purpose of this subsidy is to make aquiring information more attrative by rewarding the firm for not undertaking the projet when θ is low, beyond the punishment that β = 0 implies. Only when the punishment is not enough, ρ N (k) > Notie, though, that when the ontrator is paid for not arrying out the projet it will obtain positive rents. The reason is that in this ase the firm ould guarantee a profit of ρ N (k) by not aquiring information and never arrying out the projet. Thus, the optimal ontrat must provide higher profits when the firm is informed and this is the reason why ρ P (k) is inreasing in ρ N (k) and ρ P (k) > ρ N (k). This last inequality also explains why subsidies are useful in this ase, as opposed to what we onluded for the ontrats studied 11 In pratie this extreme kind of punishments is unlikely to be implementable. For example, the government may learn about the realization of θ when the firm has already operated projet for some time and, therefore, this punishment might imply that the revenues an be relaimed at no legal ost. When β has a lower limit the previous proposition suggests that ρ N (k) should inrease. 26

27 in the benhmark model. In proposition 3 we showed that subsidies were not optimal sine they ould not be assoiated to speifi realizations of θ. Here ρ P (k) is only paid when θ + d, making transfers weakly inreasing in θ. Finally, notie that when the firm arries out the projet we are interpreting the payment ρ P (k) as an inrease in β(θ) and we impliitly allow for β (θ) > 1. This is without loss of generality sine it is immediate that beause we an ondition on θ, any ombination of a proportion of the projet and subsidy that leads to the same profits βθ T provides idential inentives. Of ourse, a ontrat like the previous one might not be feasible for many reasons. The most important one is the risk of what we might all as phony onessions. Suppose that the apaity of a firm to arry out might be unknown to the prinipal. A ontrat like the one desribed here might attrat firms that are not qualified just beause they expet to reeive the payment from not arrying out the projet. A similar problem would also arise in the model if firms ould ome up with projets that they know that have a deterministi value θ = 0 and propose them to the prinipal just to show that this is the value. The previous ontrat would imply that they should be ompensated, whih is learly problemati. Finally, another reason why suh a ontrat might no be realisti is the fat that when the firm gets large rents this ontrat might entail a high soial ost in some ontexts either for politial reasons (beause the firm is paid when the projet is not arried out) or due to the distortionary taxation involved, If the previous payments are not possible, depending on parameter values the government may still indue learning under a Flexible-Term onession for all k K s. In partiular, notie that for any θ + d the ontrator obtains an inrease in profits of k when it is not informed. When θ < + d, however, it is still optimal for the government to impose 27

28 the maximum penalty on the ontrator whih means that β(θ) = 0. Comparing expeted profits we obtain that the firm prefers to get informed if k G( + d). (4) Therefore, the first best will still be possible if K s G( + d) whih is onsistent with the result of the previous proposition that the first-best was implementable with ρ N (k) = 0. Otherwise, ineffiienies along the same line as the ones disussed in the benhmark ase will arise for k (G( + d), K S ]. The next proposition haraterizes the ontrat that implements the seond best in this ase. Proposition 5. The optimal Flexible-Term Contrat when payments for not arrying out the projet are not possible an be haraterized as: If k K ft and θ θ ft then β (θ) = +ρ P (k) θ ; θ < θ ft then β (θ) = 0, where θ ft = max [ + d, G ( )] 1 k and k ρp (k) = 1 G(θ ft ). If k > K ft then β =. E(θ) The threshold value K ft is defined as θ ft K ft = [θ ( + d)] g(θ)dθ K S. 0 The ontrat we desribe here is not unique and other ombinations of β(θ) may lead to the same outome. As before, the ontrat implementing the seond best must imply a maximum punishment when projets with low value of θ are implement, β = 0. When 28

29 the probability that the low realizations of θ arise and ondition (4) is unlikely to hold distortions similar to those in the benhmark problem will arise here. Some projets, those with θ [ θ S, θ ft) will not be implemented in order to penalize the firm when no information is gathered. For this reason, the value of information will be lower in this ase. As a result, for intermediate values of the ost of information, k ( K ft, K S], the firm will arry out the projet uninformed, leading to white elephants. Notie also that an important onsequene of eliminating negative payments is that the firm will obtain a higher reward when θ is high, ompared to the first best. The ost of information must be reimbursed through fewer states of the world. 7 Conluding Remarks This paper emphasizes the effets of onsidering the seletion of projets in the haraterization of the optimal onession ontrat. The renegotiation that has been a fous in the literature is often the refletion of underlying poor projet seletion. The main insight of our analysis is that when this is the ase it is optimal to transfer part of the demand risk to the ontrator in order foster the aquisition and better use of the information. Institutional frameworks that limit the losses that the firm an absorb aggravate this inentives problem. Hene, an important lesson from our analysis is that in ase of failure the firm and its debtors should only be ompensated for the present value of the onession from that point on. The inentives to aquire information on the profitability of the projet by the ontrator will depend on the ommitment power of the prinipal to suh a poliy. Our model abstrats from several important aspets. In partiular, our prinipal-agent model assumes that the projet is given. Many times, however, the projet is proposed by the firms that might arry it out. This introdues an additional reason why demand is en- 29

30 dogenous to the firm ations. Allowing for the projet to be strategially offered requires the optimal mehanism to have a sreening omponent. When this omponent is not onsidered additional distortions might arise. An illustration of that is the Castor Projet, the biggest investment in the gas system in Spain, onsisting in a submarine gas storage faility in the east oast. This projet, aimed to store up to 1.3 billion ubi meters of gas, was sponsored by a firm speialized in this kind of infrastruture. Amid the onerns about the risk of generating earthquakes, due to the loation of the storage faility lose to a tetoni fault, the sponsor/onessionary was proteted from this ontingeny by the ontrat in spite of its information advantage over the administration. The earthquakes materialized soon after the projet started and they fored the Spanish government to stop it and ompensate the firm. Finally, although we introdue a simple model of ompetition and a prourement aution our approah makes several restritive assumptions suh as a seond prie mehanism or the fat that the aquisition of information is known to all firms. A more general approah to ompetition would require the optimal mehanism to not only generate inentives for firms to aquire information but also to aggregate it in a way that minimizes the winner s ourse. Referenes Bain, Robert and Lidia Polakovi, Traffi Foreasting Risk Study Update 2005: Through Ramp-Up and Beyond, Tehnial report, Standard and Poors, Bullen, Ross, This Alarming Generosity : White Elephants and the Logi of the Gift, Amerian Literature, Deember 2011, 83 (4), pp Engel, Eduardo, Ronald Fisher and Alexander Galetovi, Highway Franhising: Pitfalls and Opportunities, Amerian Eonomi Review, May 1997, 87 (2), pp