The Simple Eonomis of White Elephants Juan-José Ganuza Universitat Pompeu Fabra and Barelona GSE Gerard Llobet CEMFI and CEPR July 13, 2017 Abstrat This paper shows that the onession model disourages firms from aquiring information about the future profitability of a projet. Uniformed ontrators arry out good and bad projets beause they are profitable in expeted terms even though it would have been optimal to invest in sreening them out aording to their value. White elephants are identified as avoidable negative net present-value projets that are nevertheless undertaken. Institutional arrangements that limit the losses that firms an bear exaerbate this distortion. We haraterize the optimal onession ontrat, whih fosters the aquisition of information and ahieves the first best by onditioning the duration of the onession to the realization of the demand and inludes payments for not arrying out some projets. 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 CEMFI, FUNCAS, Universitat de Barelona, Universitat de les Illes Balears, Universidad de Las Palmas, University of Toronto, XXXI Jornadas de Eonomía Industrial, 41 Simposio de la Asoiaión Española de Eonomía and the Transpareny in Prourement onferene at the University of Edinburgh. The seond author aknowledges the support of the Spanish Ministry of Eonomis and Competitivity through grant ECO2014-57768 and the Regional Government of Madrid through grant S2015/HUM-3491. Comments should be sent to juanjo.ganuza@upf.edu and llobet@emfi.es. 1
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 it is now ommonly 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, has sat mostly vaant; the Brisbane s Clem Jones Tunnel had less than 50% of 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, 2004. 2
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 unneessary infrastrutures. 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 that engages in a long-term ontrat with a 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 publiwork 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 projets is high, sine PPP onessions overing infrastrutures 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 even for a short horizon. In the ase of demand estimation, Bain and Polakovi (2005) 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 lose to a e 30 billion industry in 2006. In low and middle-inome ountries PPP invesment reahed US$160 billion in 2010. 3
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 0.26. A similar error persisted in the years 2 to 5. 4 The underperformane of the onessions is striking sine one of its main advantages 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 horizons and demands risk suh as water and sanitation, where renegotiation ours in 74.4% of the ases. Importantly, Guash (2004) also reports that most renegotiations 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 4 Flyvbjerg et al. (2005) analyze 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 of 0.44). They 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
the onessions are limited by a future renegotiation (while the firm appropriates the potential upside) the inentives to aquire information are redued, negatively affeting projet seletion. 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 olletion of toll fees during a limited period of time. 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 its ost. 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 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 rises 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 beomes too expensive, in terms 5
of inentives, to motivate 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. It is important to notie that our definition of white elephants is restrited to those projets for whih proper ex-ante information aquisition was optimal but it did not our. This is in ontrast with the way they are typially interpreted, where evaluation of projets like the ones mentioned earlier is arried out ex-post. The presene of unertainty inevitably implies that for some projets the osts will never be reovered but this does not imply an upfront bad projet seletion. The question that our paper addresses is how those bad projets that ex-ante ould have been effiiently sreened out by investing in information end up being built, and how standard ontrats ould be adapted to provide the proper inentives and redue their ost for the soiety. 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. When we introdue this element in the model we show that the lower 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 when fewer losses an be absorved leading to more white elephants. An important poliy reommendation of our analysis is that governments should ompensate bankrupt onessionaries aording to the value of the onession and not the inurred ost. This value an be unovered by autioning the failed onession. 6 All our analysis relies on two important assumptions. First, we take the institution of 6 In some ountries the limit on the losses takes an expliit legal form. For example, in Spain it is denoted as Responsabilidad Patrimonial de la Administraión, for whih an underwater onession is taken over by the state and the firm is ompensated aording to the ost inurred. In line with the poliy reommendation of this paper, a reent hange in the law has linked this ompensation, instead, to the present value of the ash-flows of the onession at the time of the resue. 6
onessions as given and we do not onsider transferring ownership of the infrastruture to the firm. Clearly, this alloation of risk would ahieve the first best, but it is rarely observed in pratie for several reasons, inluding among others, legal onstraints or finaning advantages of the government ompared to the firm. Seond, we assume that the firm an aquire information beyond 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 infrastruture 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 possess 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 private 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, the demand is often 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, demand risk should be absorbed by the government. Transferring risk to the firm has little effet on performane but might indue ontrat renegotiation. 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 7
(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 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 However, our main theoretial result, the haraterization of the optimal onession ontrat, relies on a powerful idea of the LPVR mehanism: the need to enrih the onession ontrat with the available information about the realized demand. We show that a onession ontrat with this feature, together with the possibility of paying for not undertaking a projet, an attain 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. Although it an be argued that a mehanism involving payments to the firm for not undertaking the projet may not be politially feasible, we believe that our approah opens a new way to think about the provision of inentives in onession ontrats when projet seletion matters. We also haraterize the seond best ontrat 7 This is beause the expeted realization of the demand is different depending on whether the ontrator is informed or not. In some sense, the demand is not ompletely exogenous to the ations taken by the ontrator. 8
when suh a ompensation is not feasible 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 analyzes the effets of limits on the losses that firms an absorb and setion 5 haraterizes the optimal flexible-term onession ontrat. Setion 6 disusses extensions of the model, inluding the effet of ompetition. 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. We assume that if this ost is inurred the exat value of θ is revealed. 9 Otherwise, the value is only revealed after investment takes plae. Throughout the paper we make the assumption that even without information it is 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 We hoose this fully informative signal for tratability reasons. But we see no reason why if the value of the projet were observed with noise the results would be qualitatively different. 9
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 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 prinipal awards the ontrator a ompensation onsisting of a proportion β [0, 1] of the returns from the projet. 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. 10 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 θ are arried out while, at the same time, not passing over soially profitable investment possibilities. When several ontrats lead to the same level of soial welfare we will assume that the government hooses the one that minimizes firm profits. 10 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
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. 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 selet only those for whih 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 bad projets are sreened out. Instead, if k > K s, it is soially optimal not to aquire information and all projets will 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 projet seletion an only be attained by hoosing β = +d < 1. 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
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 The intuition for this negative relationship an be easily explained using Figure 1, whih omputes the returns for different values of θ. The dashed line orresponds to the soial welfare generated. The dotted line omputes private profits under a onession β = As disussed before, by onstrution, profits of an informed firm are positive in this ase. +d if and only if θ θ s. Notie, however, that the value of information for the firm is lower than the value for soiety, sine the gains from avoiding bad projets low θ are smaller. 11 As a result, when k > K ( +d) a onflit arises. Providing inentives to invest in suh a ase requires lowering the profits when a bad projet is undertaken, whih implies β < +d as shown in the solid line of the figure. However, this derease in profits disourages the firm, one informed, to arry out some profitable projets with θ [θ s, θ ). The next lemma summarizes this disussion. Lemma 1. For values of k [ K ( +d), K s ) the first best annot be attained. 11 The profits from undertaking projets with θ θ s are also smaller than the soial welfare they generate. However, this differene does not affet the value of information sine for those projets the profits with and without information are the same. 12
Π θ ( + d) β θ θ s θ 1 βθ θ ( + d) Figure 1: Losses and profits depending on θ. 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 providing inentives for the firm to learn and, thus, 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 the 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 due to the lak of information 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 13
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, 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. ] β(k) Proposition 1. The optimal ontrat orresponds to if k < K ( β +d +d), (k) = β(k) if K ( +d) < k < K, otherwise, where E(θ) E I ( K) + K = E II. Notie that sine E II = K s, K < K s. Figure 2 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 [ the dotted area in Figure 1 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 14
β +d β(k) E(θ) K ( ) +d K K s k θ + d E I E II K ( ) +d K K s k Figure 2: Seond best as a funtion of k. ostly. The low value projets that are arried out in this region (when θ < + d) will be identified as white elephants, beause the firm does not have inentives to aquire information although it is soially optimal to do so. These projets that should have been sreened out are identified as the dashed area in Figure 2. 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 inur 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 might motivate governments to subsidize underwater onessions. 15
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 β result 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 ontrator will never get informed beause the value of information is preisely to eliminate those realizations of θ for whih the firm makes losses and this is something that L = 0 already guarantees at no ost to the ontrator. The optimal ontrat an again be ast in terms of the omparison of Type-I and Type-II errors. ). Proposition 2. The optimal ontrat under limited losses orresponds to where β +d (k, L) = β(k, L) E(θ) if k < K (, L), +d if K (, L) < k < K(L), +d otherwise, 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 is lower, sine K ( +d, L) inreases with L. 16
For intermediate values of k, the prinipal 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 guarantees that learning takes plae, 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 realloation of surplus towards the firm. 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 3 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, 2. White elephants are less likely, and 3. Equilibrium deision errors are smaller. 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 3: The effet of the limit in losses. The dashed line orresponds to L < whereas the solid line indiates the benhmark ase L =. 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 in whih 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 18
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 information aquisition. 5 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 pointed out that the distortions assoiated with the threat of renegotiation would be mitigated if the ontrat ould 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 the realized traffi. Highways that are 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 breaks even. In our benhmark model this kind of ontrats an be easily aommodated by assuming that β(θ). In partiular, if k = 0 the Least Present Value of Revenues mehanism implements the first best by setting β(θ)θ = 0. This mehanism removes all risk from 19
the firm and guarantees that it obtains zero profits regardless of the realization of the demand. However, when k > 0 this standard flexible-term ontrat is ineffiient in terms of providing inentives for firms to get informed. 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 loss limit and, thus, it suffers from problems similar to those disussed in previous setions. This flexible-term ontrat, however, an be improved upon if rents are provided to ompensate the ost of learning and these rents are doled out when the firm only undertakes high value projets. The next proposition shows that a flexible-term ontrat ahieves the first best if it also introdues a payment for the firm 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 the firm does not invest, it reeives a payment ρ N (k), the firm invests when θ + d, then β (θ) = +ρ P (k) θ, θ < + d, then β (θ) = 0. 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) 20
When k K s the previous ontrat onsists 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 undertaken has a low value, however, the firm is awarded a onession with β = 0 as this is an indiation that no information was aquired. Rewarding the firm when θ is high might undermine the inentives for the firm to aquire information in the first plae as it might antiipate in some ases positive profits from not aquiring information and undertaking the projet anyway. For some parameter values the punishment that β = 0 implies when θ is small might make this an irrelevant onern. When this punishment is not enough to provide inentives to aquire information inreasing β(θ) when the θ θ s does not help sine this payment is always reeived. Thus, we need to introdue a third element in the ontrat whih is a ompensation ρ N (k), when the ontrator deides not to arry out the projet. This payment works beause it inreases the wedge in profits between undertaking low value projets and not doing so and, as a result, it provides additional inentives to beome informed. 12 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 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 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 12 In pratie extreme punishments are unlikely to be implementable. For example, the government may learn about the realization of θ when the firm has already operated the 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. 21
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 in some ontexts. For example, suppose that the apaity of a firm to arry out a projet is unknown to the prinipal. A ontrat like the one desribed here might attrat firms that are not qualified just beause they expet to reeive a positive payment ρ N (k) from not arrying out the projet, without the need to invest in information. Similarly, a problem would also arise if the firm were the one proposing the projet as it ould ome up with phony onessions, ontrats that should never be undertaken, just to be ompensated for that. 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 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 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). (3) Therefore, the first best will still be possible if K s G(+d) whih is onsistent with the 22
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. 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 K ft = θ ft 0 [θ ( + d)] g(θ)dθ K s. Notie that the ontrat we desribe here is not unique and other ombinations of β(θ) may lead to the same outome. When the probability that the low realizations of θ arise and ondition (3) 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. 23
6 Extensions of the Results In this setion we extend the disussion of the model in three diretions. We start by analyzing the effets of onsidering the dead-weight loss assoiated with the market power neessary for the firm to reoup the investment during the onession period. We later study the ase in whih ex-ante, without information, it is not worthwhile to undertake the projet. Finally, we show that ompetition generates similar distortions to the ones analyzed in the one firm ase. 6.1 Distortions and Externalities In the benhmark model we have interpreted β as the duration of the onession ontrat. That is, during a proportion β of the future, the firm ould reap all the returns from the projet. This simple setup has two main limitations. First, market power typially generates a loss that neither the firm nor the soiety an appropriate. Seond, a onession ontrat omprises many terms like the prie and the duration, many ombinations of whih lead to the same β but have different welfare impliations. The demand model that would be onsistent with our assumptions would be one in whih D(p) = 1 if the prie p θ and D(p) = 0 otherwise. Obviously, in this ase no distortion would arise and, ontingent on prodution, surplus would always equal θ. Furthermore, any ombination of a duration of the onession, denoted as γ, and prie, p, suh that γp is onstant would be equivalent. In more general ontexts the two previous limitations might beome relevant. We will not disuss here the trade-off between the prie and the duration of the onession as this is an issue that has been studied at length in the literature, for example in the ontext of patent design. 13 Instead, we fous on the effets of introduing stati distortions. 13 Two lassial referenes of the onditions neessary for one dimension to be less distortionary than 24
Suppose that a prie p > 0 leads to profits θ for the firm and a distortion δ while this onession is in plae. Assume also that absent a onession (when p = 0) onsumer surplus implies that θ generates a total surplus sθ with s 1. Total welfare an, thus, be written as W = β(1 δ)sθ + (1 β)sθ = (1 βδ)sθ σθ, where, (1 δ)s 1 implies σ 1. As in the benhmark model, the firm would have exessive inentives to invest if σ +d and, hene, β 1 when k = 0. As a result, when k > 0 similar effet to the ones disussed in that ase will emerge here. 6.2 Ex-ante Unprofitable Investments A maintained assumption throughout the paper was that E(θ) + d, meaning that without information the projet had a net positive expeted value. The aquisition of information was useful to sreen out bad projets that without it would be undertaken. It is reasonable to believe that the previous assumption aptures the natural default ase. The reason is that the projet under onsideration is likely to be the outome of a wider seletion proess in whih alternatives with lower expeted value are sreened out. Nevertheless, we now disuss how the results hange if E(θ) < + d. From a soial standpoint, in this ase the projet should be undertaken if and only if information has been aquired and θ +d. As a result, the aquisition of information is soially valuable if k K s 1 [θ ( + d)] g(θ)dθ. +d As in the benhmark model, under a onession ontrat, hoosing a β = imple- +d ments the first best when k is small. For k suffiiently large there is no distortion either, sine the projet is never arried out. For intermediate values of k, as the ase disussed in the main text, the firm laks inentives to aquire information. As shown in Figure 1, when θ θ s the private returns when β = +d the other are provided by Klemperer (1990) and Gilbert and Shapiro (1990). are smaller than the soial returns. As a 25
result we have two situations. When k is relatively small, β must be distorted upwards as this inreases the rents for the firm when it aquires information and arries out the projet. Notie that this higher β leads to undertaking projets that are not soially effiient sine θ < θ s. When k is relatively large, the high β neessary implies that many bad projets would be arried out and it is soially preferable to not aquire information and not undertake any projet. One impliation of this disussion is that the firm never inurs in losses in the equilibrium path. Either the projet will not be undertaken or only those that have a private positive return will be arried out. Thus, limits on the losses or the antiipation of the renegotiation of the onession play no role have no effet on the inentives to aquire information. Finally, the haraterization of the flexible-term ontrat that attains the first best is simple. The funtion β(θ) must satisfy three onditions. When θ < θ s then β(θ) = 0 in order not to undertake ineffiient projets. When θ θ s and k K s it has to satisfy the ondition 1 +d [β(θ)θ ] g(θ)dθ = k so that the firm has inentives to aquire information. Finally, when θ θ s, β(θ) θ so that undertaking good projets is profitable. Of ourse, the optimal ontrat is not uniquely defined. Also, notie that this ontrat is simpler than the one in the main text whih required payments for not arrying out the projet. There is an intuitive reason for that. The idea of flexible-term ontrats is to reward the firm when the projet is worthwhile. In the baseline model, this reward makes the ex-ante problem of aquiring information worse. In this ase, however, rewarding the firm when θ is high provides more inentives to aquire information in order to undertake good projets. 26
6.3 Competition Our benhmark model assumes that only one firm an arry out the projet. However, most onessions are awarded ompetitively through an aution. To address this issue, 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 setions 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 suppose 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 observable but not ontratible before plaing the bid. The timing of the model is now as follows. In the first stage, the government sets the reserve prie. Seond, firms deide simultaneously whether to pay k to get informed or 27
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 the value of the 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, both firms get informed. Then, eah firm learns the real θ and bids β i =. As a result, their profits are equal to k. Seond, none θ of the firms gets informed. In that ase, firms will bid aording to the expeted value, β i = /E(θ) as long as β > /E(θ) and they 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. 28