metadata: authors: 0: author: Estache,Antonio
1: author: Iimi,Atsushi
count: World
docna: 0: docna: Bidders' entry and auctioneer's
            rejection : applying a double selection model to road
            procurement auctions
docty: Policy Research Working Paper
subtopic: Social Policy,Legal Products,Judicial System Reform,City to City Alliances,Public Sector Economics,National Urban Development Policies & Strategies,Regional Urban Development,Urban Economics,Competition Policy,Legal Reform,Flood Control,Legislation,Regulatory Regimes,Urban Economic Development,Competitiveness and Competition Policy,Public Finance Decentralization and
            Poverty Reduction,Transport Services,Urban Communities
teratopic: Private Sector Development,Public Sector Development,Macroeconomics and Economic Growth,International Economics and Trade,Finance and Financial Sector Development
abstracts: cdata!: Limited competition has been a serious
            concern in infrastructure procurement. Importantly, however,
            there are normally a number of potential bidders initially
            showing interest in proposed projects. This paper focuses on
            tackling the question why these initially interested bidders
            fade out. An empirical problem is that no bids of fading-out
            firms are observable. They could decide not to enter the
            process at the beginning of the tendering or may be
            technically disqualified at any point in the selection
            process. This paper applies the double selection model to
            procurement data from road development projects in
            developing countries and examines why competition ends up
            restricted. It shows that bidders are self-selective and
            auctioneers also tend to limit participation depending on
            the size of contracts. Therefore, limited competition would
            likely lead to high infrastructure procurement costs.
repnme: repnme: Bidders' entry and auctioneer's
            rejection : applying a double selection model to road
            procurement auctions
display_title: Bidders' entry and
            auctioneer's rejection : applying a double selection
            model to road procurement auctions
listing_relative_url: /research/2009/03/10315783/bidders-entry-auctioneers-rejection-applying-double-selection-model-road-procurement-auctions
topicv3: Government Procurement m1326093 957,Transport m1326661 135,Urban Development m1327371 699,Public Procurement and Competition
            m1327470 2105,Road Construction m1505347 4030
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Public Sector Development,Macroeconomics and Economic Growth,International Economics and Trade,Finance and Financial Sector Development
no_of_pages: 26
author_keys: 0: author_key: 98672
1: author_key: 914707
model_extractions: WPS4855 Policy ReseaRch WoRking PaPeR 4855 Bidders’ Entry and Auctioneer’s Rejection Applying a Double Selection Model to Road Procurement Auctions _Antonio Estache Atsushi Iimi_ The World Bank Finance, Economics and Urban Development Department Economics Team March 2009
Policy ReseaRch WoRking PaPeR 4855

# **Abstract**

Limited competition has been a serious concern in infrastructure procurement. Importantly, however, there are normally a number of potential bidders initially showing interest in proposed projects. This paper focuses on tackling the question why these initially interested bidders fade out. An empirical problem is that no bids of fading-out firms are observable. They could decide not to enter the process at the beginning of the tendering or may be technically disqualified at any point in the selection process. This paper applies the double selection model to procurement data from road development projects in developing countries and examines why competition ends up restricted. It shows that bidders are self-selective and auctioneers also tend to limit participation depending on the size of contracts. Therefore, limited competition would likely lead to high infrastructure procurement costs.

This paper—a product of the Economics Team, Finance, Economics and Urban Development Department—is part of a larger effort in the department to understand and enhance efficiency and effectiveness in public procurement for infrastructure. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at aiimi@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **BIDDERS’ ENTRY AND AUCTIONEER’S REJECTION:**

# **APPLYING A DOUBLE SELECTION MODEL TO ROAD PROCUREMENT AUCTIONS**

Antonio Estache Université Libre de Bruxelles Atsushi Iimi<sup>§</sup> World Bank (FEU) Key words: Public procurement; auction theory; endogenous bidder entry; infrastructure development.

JEL classification: D44, H54, H57, C21, D21.

§ We express our special thanks to Japan International Cooperation Agency (former Japan Bank for International Cooperation (JBIC) ODA Operations) for their collaboration in data collection and their insightful comments on an earlier version of this paper. We are also grateful to Decio Coviello, Marisela Montoliu Munoz, Tomás Serebrisky and Tina Søreide for their various suggestions and comments. We also thank many seminar participants in the Chaire Bernard Van Ommeslaghe Conference at the Université Libre de Bruxelles.
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# **I. INTRODUCTION**

Infrastructure procurement is still a challenging task for developing country governments. The limited degree of competition remains among the major concerns (Foster, 2005; NOA, 2007; Estache and Iimi, 2008a). A fundamental problem for auctioneers, namely executing agencies, is how to contain government procurement costs while ensuring the good quality of public work would be delivered. Even though competitive bidding is now commonly required in public procurement systems, participants are often limited because infrastructure projects tend to be highly valuable, complex and customized.

Traditional auction theory suggests that increased competition would lower procurement costs under the fixed- _n_ approach. Although how the degree of competition would affect the auction outcome will depend on model, this has been confirmed in many empirical auctions (e.g., Brannman _et al_ ., 1987; Paarsch, 1992; Gupta, 2002; Estache and Iimi, 2008a). In the independent private value paradigm, by which our traditional ODA projects could be characterized, the winning bid should tend to approach the lowest possible procurement price, as the number of participants in an auction increases.<sup>1</sup> Therefore, competition is in principle considered welcome for auctioneers, and the issue examined in the current paper is closely related to the results derived by Bulow and Klemperer (1996), discussing the value of an extra bidder in an auction in terms of the buyer’s expected traded prices.

Importantly, however, bidders’ participation is endogenous. On one hand, potential bidders themselves will decide whether or not to enter the tendering, depending on their endowments,

> 1 How to determination the paradigm must of necessity defer to individual empirical works (e.g., Paarsch, 1992; Bajari and Hortaçsu, 2003). The ODA-related infrastructure project procurement auctions may be more likely to be characterized by the independent private value paradigm, because auction-specific asymmetric uncertainty among bidders plays a more important role to determine the individual bid prices than symmetric uncertainty does. Typical are labor costs of individual firms. Even though the same amount of inputs is required to implement a project, unit costs (e.g., wages and equipment prices) are different across firms (Bajari _et al_ ., 2006). Also those private factors remain different even after the contract is awarded. By contrast, political instability and regulatory credibility are considered as a commonly uncertain component. These often affect the publicprivate partnership (PPP) infrastructure projects. However, in our traditional ODA projects to procure only specific construction works or equipment, these are less important than firm individual cost factors. Furthermore, ODA contracts are not supposed to be resold once awarded.
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rivals’ behavior and the size and nature of projects being auctioned. On the other hand, auctioneers also desire to limit competition in the sense that they might disqualify some of the initial applicants prior to taking their price bids into account. Project owners often want to exclude from the selection process those who would likely fail to fulfill the agreed contract.

Without doubt, the number of bidders observed at the final price evaluation stage results from a sequence of choices made by prospective firms and an auctioneer. For this reason, partial observability must emerge as a potential empirical problem. One can observe bids only if firms participate in the tender and are qualified through prerequisite conditions. Auction theory has discussed the endogeneity issue associated with bidders’ entry (e.g., McAfee and McMillan, 1987; Levin and Smith, 1994; Menezes and Monteiro, 2000). Basically, it shows that high entry costs would reduce the optimal number of bidders, and bidders would enter until their expected profits are driven to the entry cost. Unfortunately, however, the selection is rarely singleton in practice. Auctioneers can be selective as well. Moreover, even qualified bidders may desire to withdraw their proposal in the middle of the process.

The current paper collects data on potential bidders from public procurement auctions for road development projects in developing countries and aims at tracking their sequential decisions toward the final decision about who would be the awardee. In general, it is empirically uneasy to identify potential bidders, simply because they are not observable.<sup>2</sup> The current paper pays attention to those who purchased prequalification or bidding documents as a good set of serious prospective bidders. They may or may not participate in the tendering, as will be described later. The paper, using the sequential-response model (Amemiya, 1975; Maddala, 1983), examines how auctioneers and individual firms decide whether or not to proceed to the next step toward the final price bid evaluation stage. Then,

> 2 In the existing endogenous entry auction literature, this difficulty tends to be avoided by relating the realized (not potential) number of bidders to explanatory variables in a Poisson or negative binomial regression model (e.g., Li and Perrigne, 2003; Li and Zheng, 2006; Ohashi, 2008; Estache and Iimi, 2008b). Otherwise, one can assume that those who participated in a series of auctions at least once in the past would constitute a set of potential bidders.
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the equilibrium bid function is estimated by the Heckman (1979) and Lee’s (1978) two-step estimation method with a double selection process.

The remaining paper is organized as follows. Section II describes the traditional public procurement procedure and overviews the behavior of potential and actual bidders in our road procurement data. Section III develops the empirical methods and summarizes our used data. Section IV presents the main results and discusses some policy implications.

# **II. AN OVERVIEW OF PARTICIPATION DECISIONS BY BIDDERS AND AUCTIONEERS IN ROAD PROCUREMENT**

Public road projects are traditionally procured through the first-price sealed-bid competitive tenders. Notably, however, there are a variety of procurement systems involving different institutional elements. For instance, some auctions invite only domestic companies, while others accept international enterprises as well. But the most important difference in terms of auction design may be that some auctions adopt the strict lowest price criteria where only the price bids are compared, while others account for “quality,” which refers to anything the auctioneer cares about other than prices.<sup>3</sup> A typical example is prequalification. In largescale infrastructure projects, the technical evaluation prior to comparing prices is normally required in order to ensure the quality of the object or public work, the contract cost agreed, and the period designated.

From the auctioneer’s point of view, apparently, there is a tradeoff between price and quality if the latter is costly for firms to produce and attain; higher quality, higher prices. In addition, if quality is also costly to prepare before the auction, the optimal number of bidders that are allowed to enter would decline in the presence of increased entry costs, whence limiting

> 3 There are a certain amount of theoretical works on multidimensional auctions. They show that the two-stage bid evaluation system can implement the optimal mechanism maximizing auctioneer’s expected profits (Che, 1993; Cripps and Ireland, 1994). However, it is still far from applicable to practice.
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competition and raising the equilibrium bid. Moreover, if there are a limited number of companies that could meet highly specific qualification requirements, then the competition would also become narrow.<sup>4</sup> Too exclusive conditions might even be considered corruption.<sup>5</sup> From the bidder perspective, they must be of necessity self-selective for a number of reasons. The fundamental reason is that potential contractors are under resource constraints to a larger or lesser extent. They may not be technologically competent enough to apply for a complex contract.<sup>6</sup> Even though they are potentially able to implement that project, they may not tentatively have available resources for new contracts because they are already devoted to other development projects elsewhere. In addition, if the entry cost is too high, bidders may decide not to enter the tendering process, though having shown interest. Finally, the bidders’ strategy would also be influenced by rivals’ entry and bidding behavior. In theory, it could be affected if bidders are asymmetric,<sup>7</sup> or if bidders have private signals but do not ex ante know the true common value of the object being auctioned.<sup>8</sup> Hence, bidders and auctioneers have various different reasons for not participating or not allowing them to participate in the tendering process. Our data uncover the typical auction process for road construction and rehabilitation works, during which the applicants gradually shrank from 13 to 4 on average (Figure 1). At the very beginning of the process, auctioneers usually publish tender notices. About 13 companies or consortia per contract showed interest 4 See Estache and Iimi (2008b) for more discussion.

5 A crucial shortcoming of multidimensional auctions is that the award process would be less transparent and more vulnerable to corruption; authorities can easily exploit their excessive discretion (Klein, 1998; Ware _et al_ ., 2007; Estache _et al_ ., 2008).

6 One of the solutions to this resource constraint problem is joint bidding. Bidders can overcome the possible prerequisites by pooling their financial and managerial resources with each other (e.g., Moody and Kruvant, 1988; Hendricks and Porter, 1992; Iimi, 2004).

7 Asymmetric auction theory predicts that a weaker (fringe) bidder tends to bid more aggressively in the presence of a strong (incumbent) bidder. Maskin and Riley (2002) shows that if a weak bidder faces a strong bidder rather than another weak bidder, he responds with a more aggressive bid distribution in the sense of stochastic dominance. The empirical evidence is supportive of this (e.g., De Silva _et al_ ., 2002, 2003; Estache and Iimi, 2008c).

8 Under the common value paradigm, competition may increase the equilibrium bid due to the winner’s curse effect (e.g., Milgrom and Weber, 1982; Paarsch, 1992; Klemperer, 1998).
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and purchased the relevant prequalification or bidding documents. If prequalification is adopted, about 10 potential bidders would apply for it. Then, about two-thirds are qualified. At this stage, only 6–7 bidders remain. About one bidder may decide not to submit a price bid for some reason, though prequalified. After the staged process involving the detailed technical evaluation prior to opening the price bids, only four price bids are evaluated and compared at the final stage. In our sample, the majority of auctions adopted the two-envelope procedure, in which all (qualified) bidders are requested to submit both price and technical bids simultaneously and the auctioneer opens the price bid only if the corresponding technical bid is substantially responsive to the bidding documents and other technical requirements. As the result, the degree of competition tends to be rather limited at the very end of the auction process.

Figure 1. Numbers of Potential and Actual Bidders in Road Procurement Auctions <!-- Start of picture text --> 14<br>12 (–3.1)<br>10<br>8 (–3.6)<br>13.1 (–0.7)<br>6 (–1.6)<br>9.9<br>4<br>6.4 5.6<br>2 4.0<br>0<br>Purchasing Applying for Prequalified Submitting Price<br>PQ PQ if PQ is if PQ is bids evaluated<br>documents adopted adopted after<br>technical<br>qualification<br>Average number of firms/consortia<br><!-- End of picture text --> Source: Author’s calculation.

Because the intensity of competition changes along the bidding procedure, the relationship between the bid strategy and competition also varies depending on the stage of the selection process. Figure 2 illustrates the competition effect when it is measured at the beginning of the tender process, i.e., the number of firms that purchased prequalification or bidding documents. Figure 3 depicts the competition effect at the final price comparison stage. Of course, both ignore partial observability; one cannot observe bids from firms that not participated, though showed interest. But the comparison between them indicates that Figure 3 ignores many unrealized bids that could have been scattered where the horizontal axis is
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greater than seven if they were observed. It suggests that without controlling for the sample selection bias, the empirical competition effect would be biased.

<!-- Start of picture text --> Figure 2. Potential Competition and Bids Figure 3. Final Competition and Bids<br>10 10<br>9 9<br>8 8<br>7 7<br>6 6<br>5 5<br>4 4<br>3 3<br>2 2<br>1 1<br>0 0<br>0 5 10 15 20 25 30 0 5 10 15 20 25 30<br>Number of firms/consortia who purchased PQ documents Number of firms/consortia whose price bids are evaluated after all<br>Source: Author’s calculation. Source: Author’s calculation.<br>Evaluated bid / Engineering cost estimate Evaluated bid / Engineering cost estimate<br><!-- End of picture text -->

# **III. THE EMPIRICAL MODELS**

The following sequential decisions made by an auctioneer and potential bidders are considered. Suppose that _L_ firms purchased prequalification and/or bidding documents. These constitute a set of potential bidders, out of which _M_ firms applied for prequalification if the prequalification process is introduced, or just entered into the price competition if prequalification is omitted. This is the first selection made by each bidder of  ,1  , _L_  , denoted by _d_ 1. Then, the auctioneer qualifies _N_ firms from actual applicants  ,1  , _M_  due to technical reasons. Disqualification occurs at either the prequalification or technical evaluation level. This is the second selection, denoted by _d_ 2. Even though qualified, bidders can still choose not to proceed to the final price comparison stage. Some qualified bidders in fact cease participating in the auction, possibly because of unexpected financial and equipment constraints. But such cases are relatively rare, as shown in the previous section. Hence, the model focuses on only two major decision nodes: (i) whether firms apply for the bidding process, and (ii) whether bidders are qualified and advance to the price competition.
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The selection rules are as follows: where _d_ 1<sup>*</sup> and _d_ 2<sup>*</sup> are latent variables but have dichotomous observable realizations, _d_ 1 and _d_ 2, respectively. _Z_ is a vector of bidder- and auction-specific characteristics determining the selection mechanisms. The two error terms are assumed to follow a multivariate normal distribution with zero means and variances equal to unity. Potentially, the error terms can be 2 correlated with one another. Denote this by _Cov_  1<sup>,</sup>  2    . One might expect that an auctioneer disqualifies firms that have certain common unobserved characteristics, which could also systematically encourage bidders to enter into the auction. In this case, the correlation _ρ_ will be negative.

Given the two selections, each bidder of  ,1  , _N_  submits the following conventional symmetric equilibrium bid (e.g., Porter and Zona, 1993; Gupta, 2002; Iimi, 2006): ' ln _BID_  _X_  _u_ (3) where _X_ is composed of bidder- and auction-specific variables that influence firms’ underlying cost parameters and control for heterogeneity among projects to be auctioned. _BID_ is the evaluated bid price. This is observed only for firms that entered and were qualified. Consequently, the ordinary least squares (OLS) estimation would lead to the sample selection bias if Equations (1) and (2) are significant (Lee, 1978; Heckman, 1979).
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Following the existing literature focusing on the double or generalized selection process (e.g., Poirier, 1980; Lee, 1983; Tunali, 1986; Mohanty, 2001), Equation (3) can be consistently estimated by correcting the two selectivity biases: _i_ , _j_  2,1and _j_  _i_ .  is the standard normal density function and  is the cumulative normal distribution function. _B_ is the bivariate standard normal distribution function.

To estimate Equation (4), the two-step method is adopted. The first stage is estimated by a censored bivariate probit model because of partial observability, because the second selection rule _d_ 2 is observed only if bidders apply for the prequalification process, i.e., _d_ 1  1 . The corresponding log likelihood function is: The first term is associated with the probability that a bidder decides not to apply for the process. The second represents the case that a bidder determines to enter into the auction but does not proceed to the price comparison stage. The last expression is the probability that a bidder is qualified and its bid is evaluated after all.

Given estimated parameters,<sup>ˆ</sup> 1 and<sup>ˆ</sup> 2 are calculated and used for the second stage. Then, Equation (4) can be estimated by OLS. This two-step estimator will be consistent, and the standard errors are corrected with the possible bias into account, which is mainly caused by the additional variance of<sup></sup> 1<sup>and</sup>  2 added to remove the selection bias. The asymptotically consistent mean square error is:
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where<sup>_v_</sup> _i_ is the residual from the OLS regression of Equation (4), and the additional error is To specify the equilibrium bid function in Equation (3), _X_ is composed of four types of project- and bidder-specific characteristics: (i) the number of bidders participating in an auction, which is often referred to as _N_ , (ii) project-specific observables, such as length of roads ( _LENG_ ), number of lanes ( _LANE_ ), engineering cost estimates ( _COST_ ) and expected contract duration ( _MONTH_ ), (iii) country-specific fixed effects, and (iv) observable bidder attributes. For the last, a set of dummy variables representing bidder nationalities are used to control potential heterogeneity across bidders. As one can expect, whether bidders are foreign or domestic is among the most important determinants of the bidding equilibrium strategy in large-scale development projects.

Regarding the first variable _N_ , it must be noted that we choose the number of bidders that were qualified if prequalification was applied and stepped in the price competition stage. If prequalification is not adopted, _N_ is simply the number of firms submitting bids. _N_ is expected to capture the competition effect particularly in the independent private value paradigm. Notably, this is comparative statics in the conventional fixed- _n_ approach; more competition would lead to lower procurement costs.<sup>10</sup> In auction theory, the endogeneity of _N_

> 9 See Tunali (1986) for a full description.

> 10 It is still theoretically possible to characterize our auctions as the common value paradigm, in which the equilibrium bid could increase with the number of bidders. However, there is little evidence supportive of this in our data, regardless of functional forms. A significant negative relationship between the bids and the number of bidders was found even in a partially nonparametric specification (Estache and Iimi, 2008a). In the current
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is another important question for considering competitiveness (e.g., McAfee and McMillan, 1987; Levin and Smith, 1994; Bajari _et al_ , forthcoming). At least from the empirical point of view, however, a necessary question may be whether _N_ is common knowledge among bidders, whatever it represents. Our defined _N_ is the best proxy in this regard. In the practical ODA procurement circumstances, serious tenderers are likely to share a good sense of how many rivals are remaining for the final price competition, either through the formal prequalification result publication and informal business relationship. Therefore, the number of bidders that were prequalified and submitted price bids is considered the best information of _N_ known by tenderers.<sup>11</sup> Following the existing literature (e.g., Porter and Zona, 1993; Bajari _et al_ ., 2006; and Price, 2008), two instruments are used for a vector of selection determinants, _Z_ .<sup>12</sup> One measure is the total amount of contracts—in our sample—awarded to each firm in the three-year period before a particular contract is auctioned ( _BKLG_ ). If a bidder forms a joint venture, the average backlog among consortium members is used. Another variable to complement this is the amount of total transport ODA disbursed to each country in the three-year period prior to the auction ( _CAID_ ).<sup>13</sup> The basic idea behind these variables is that if prospective firms are already devoted to other development projects elsewhere, fewer bidders would be willing to bid on further new works because they might be too busy. An implicit assumption is that firms are resource-constrained, which will in fact be verified in the following analysis.

paper, the competition effect is specified in logarithmic form, because it is known that the mapping between winning bids and the number of bidders is never linear (Rezende, 2005) and the logarithmic models often better fit actual auction data (e.g., Porter and Zona, 1993; Gupta, 2001, 2002).

> 11 Technically, our _N_ is different from the sum of _d_ 2 _a_ and the sum of _d_ 2 _b_ as well. It represents the number of prequalified bidders bud may include those who are disqualified technically in the pre-stage of price bid evaluation. This is the case where the two-envelope procedure is adopted. In this system, all potential bidders are requested to submit both price and technical proposal and an auctioneer opens the price bids only if the submitted technical proposal meets the required standards. It will play the similar role as prequalification, but the order is difference and the scope of the examination may be more technical (see Estache and Iimi (2008b) for more discussion on this).

> 12 _X_ is also part of _Z_ except for _N_ , because at the preselection stage, participants may not be sure how many firms would finally decide to apply for it.

13 Our sample merely represents several percent of total ODA allocated to the transport sector all over the developing world. Therefore, _CAID_ is expected to capture the broader market conditions than _BKLG_ . The used aid data come from the OECD Creditor Reporting System database.
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Table 1 shows the summary statistics. Our sample covers about 325 potential bidders that are interested in one of the 31 road procurement auctions under 11 projects in nine developing countries.<sup>14</sup> 70 percent of them applied for the tendering process. 184 firms are identified as those who were technically evaluated, and about 64 percent passed the technical examination. There were 117 bidders that were technically qualified, but not all of them participated in the price competition; only 84 percent did. Therefore, we observe 98 winning and losing bids, of which the average is about 23 million U.S. dollars. Note that both winning and losing bids are equally informative to estimate the equilibrium bid function, because the auction format normally used for infrastructure project procurement is the standard first-price sealed-bid auction.

The contracts differ considerably in financial and technical terms. While lower bids are less than 0.4 million U.S. dollars, high bids may exceed 100 million U.S. dollars. The average length of roads is about 40 km, but it ranges from 1 km to 280 km. The number of lanes also varies from two to six. The average project duration is estimated at 31 months. The average of total contract amounts obtained by a firm in the three-year period prior to the auction is about 8 million U.S. dollars. But again, there is huge variation; some firms were awarded several similar projects in recent years, and others not. In addition, each recipient country seems to receive a considerable amount of aid in the transport sector alone. Note that the last is a country-specific but time-variant variable.

14 Our sample originally covers about 450 potential bidders but is reduced to 325 due to missing relevant data.
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<u>Table 1. Summary Statistics</u>

|Variable|Abbr.|Obs|Mean|Std.Dev.|Min|Max|
|---|---|---|---|---|---|---|
|Evaluated bid 1/|_BID_|98|22.70|23.90|0.37|115.00|
|Dummy for applicants to the process|_d_1|325|0.70|0.46|0|1|
|Dummy for the technically qualified|_d_2_a_|184|0.64|0.48|0|1|
|Dummy for bidders of which bids are compared|_d_2_b_|117|0.84|0.37|0|1|
|Number of bidders proceeding to the price bidding stage|_N_|325|5.74|1.92|2.00|11.00|
|Length of roads (km)|_LENG_|325|39.59|50.50|0.90|278.55|
|<br>Number of lanes|_LANE_|325|2.95|1.29|2.00|6.<br>00|
|Engineering cost estimate 1/|COST|325|33.12|48.83|0.39|176.74|
|<br>Estimated contract duration (months)|_MONTH_|325|31.12|13.81|9.00|45.00|
|Firm's backlog in the past three years 1/|_BKLG_|325|7.78|24.40|0.00|189.00|
|Totaltransport aidreceived by the project country1/|_CAID_|325|410.89|318.82|5.73|1,000.97|
|1/ In millions of constant 2000 U.S. dollars.|||||||

Source: Author’s calculation.

# **IV. ESTIMATION RESULTS AND IMPLICATIONS**

Before presenting the equilibrium bid equation estimated by the two-step double selection technique, the sequential response model is performed to examine how prospective firms determine to participate in each step of the auction and how the auctioneer rejects some of the applicants. For this, the second decision _d_ 2 is separated into two stages. First, the auctioneer can determine to technically qualify each applicant prior to the price comparison; this process is denoted by _d_ 2 _a_ . Then, qualified bidders can decide whether to proceed to the price comparison. This is denoted by _d_ 2 _b_ . It must be noted that _d_ 2 _a_ is the decision making on the auctioneer side, while _d_ 2 _b_ as well as _d_ 1 are primarily determined by bidders. Assuming the normal distribution, the probabilities can be written as: Since these are sequential decisions, the parameters can be estimated by performing the probit model with only relevant subsample in each case (Amemiya, 1975; Maddala, 1983). An important assumption for these estimators is obviously that the random factors influencing responses at individual stages are independent.
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In our data, 325 firms constitute a set of potential bidders,<sup>15</sup> out of which 228 decided to apply for the selection process. Then, prior to the following price competition, at least 117 and 67 bidders were technically qualified and disqualified, respectively.<sup>16</sup> Out of the qualified bidders, 98 firms actually decided to proceed to the final tendering process and thus 98 price bids are observable in our data.

Table 2 presents the probit results.<sup>17</sup> There is a noticeable contrast between the auctioneer’s and bidders’ behavior related to auction participation. Bidders are more likely to enter in the tendering when their potential backlogs, which are measured by either _BKLG_ or _CAID_ , are considered moderate. This is consistent with the previous literature. It implies that bidders have certain capacity constraints. On the other hand, auctioneers would be more likely to qualify bidders that have more backlogs. This must reflect the tendency toward more experienced contractors. This is not surprising, because the prequalification process normally requires prospective bidders to have experienced similar development projects in the past. And intuitively, auctioneers may normally be comfortable contracting with incumbents.

These results highlight an important challenge in procuring infrastructure projects: Potential contractors are resource-constrained, but auctioneers may prefer to contract with those who have undertaken many other development projects. As the result, the market competition at the final stage will tend to be limited. But then the expected contract amount will increase due to lack of competition among contenders, and market concentration may also be of potential concern.

> 15 Only 252 observations are used for the first probit model, because one of the explanatory variables takes the same value for 73 cases. These are perfectly predicted in our specification.

> 16 44 observations are not used for the second probit model, because the prequalification results are unavailable in these cases.

> 17 Note that many country- and nationality-specific fixed effects are omitted because there are many cases where the fitted probability that one of the country or bidder nationality dummy variables equals unity is exactly either one or zero.
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Other than the backlog variables, it is found that larger road projects would attract fewer bidders. It is because firms that can undertake large-scale projects are limited due to their inevitable resource boundaries; the coefficients of _LENG_ , _LANE_ and _COST_ are broadly negative and significant for the bidder’s entry decisions _d_ 1 and _d_ 2 _b_ . It is also because auctioneers have a propensity to put more emphasis on bidders’ technical capabilities and past experiences when contracting out a large project. Thus, the probability that an auctioneer disqualifies an applicant would increase with the size of contract holding everything else constant. In the model for _d_ 2 _a_ , again, _LENG_ , _LANE_ and _COST_ have negative coefficients.

<u>Table 2. Binary Response Model for Bidders’ Participation</u>

|Dependent variable|_d_1|_d_1|_d_2_a_|_d_2_a_|_d_2_b_|_d_2_b_|
|---|---|---|---|---|---|---|
|ln_LENG_|–0.046|–0.371 <sup>**</sup>|–0.254 <sup>**</sup>|–0.560 <sup>**</sup>|–0.856 <sup>***</sup>|–0.713 <sup>***</sup>|
||(0.094)|(0.152)|(0.109)|(0.287)|(0.321)|(0.274)|
|ln_LANE_|–1.019 <sup>**</sup>|–0.194|–0.498|–1.613 <sup>**</sup>|–1.627 <sup>*</sup>|–1.910 <sup>**</sup>|
||(0.402)|(0.538)|(0.450)|(0.790)|(0.903)|(0.850)|
|ln_COST_|–0.068|–0.323 <sup>**</sup>|–0.192 <sup>*</sup>|–0.187|–0.115|–0.329|
||(0.105)|(0.133)|(0.119)|(0.149)|(0.185)|(0.302)|
|ln_MONTH_|–0.308|1.317 <sup>***</sup>|0.163|0.850|–1.448|3.220|
||(0.299)|(0.456)|(0.358)|(0.763)|(1.118)|(3.684)|
|ln_BKLG_|||0.024 <sup>***</sup>|0.019 <sup>**</sup>|0.005|0.013|
||||(0.007)|(0.008)|(0.012)|(0.012)|
|ln_CAID_|–0.093|0.059|–0.104|0.005|–0.781 <sup>**</sup>|–3.144 <sup>*</sup>|
||(0.081)|(0.138)|(0.104)|(0.506)|(0.317)|(1.673)|
|Constant|3.113 <sup>***</sup>|–0.291|2.225 <sup>**</sup>|3.119 <sup>*</sup>|15.508 <sup>***</sup>|13.678 <sup>***</sup>|
||(0.844)|(1.279)|(1.025)|(1.846)|(4.676)|(4.300)|
|Obs.|252|252|184|184|117|117|
|Wald-chi2|68.23 <sup>***</sup>|145.38 <sup>***</sup>|27.48 <sup>***</sup>|57.98 <sup>***</sup>|21.46 <sup>***</sup>|42.03|
|No. of country dummies|(0)|(3)|(0)|(4)|(0)|(2)|
|No. of bidder nationality dummies|(0)|(0)|(0)|(7)|(0)|(5)|
|Chi2 test statistics:|||||||
|H0: Coef. of country and bidder<br>nationalitydummies_=_0||61.89 <sup>***</sup>||43.24 <sup>***</sup>||8.38|

Note: The dependent variable is the bidder's entry selection at each stage. The robust standard errors are shown in parentheses. *, ** and *** indicate the 10%, 5% and 1% significance levels, respectively.

Source: Author’s calculation.

Turning back to the formal selection model we analyze, two main decision nodes are focused on: _d_ 1 and _d_ 2. _d_ 2 _a_ and _d_ 2 _b_ can be considered to have been merged. Notably, however, 2 is _d_ supposed to represent mainly the former decision by auctioneers ( _d_ 2 _a_ ), because the number of bidders that were qualified but did not participate in the price competition is much small in our data. It is also noteworthy that when estimating a censored bivariate probit model for _d_ 1 and _d_ 2 as the first stage regression, the two error terms can be correlated with one another unlike the above sequential response model. Table 3 shows the results, which are broadly
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consistent with the sequential response models estimated above; potential bidders are faced with resource constraints and often decide not to enter the tender especially when the contract amount is large. The coefficient of ln _COST_ is negative, and the coefficient of ln _CAID_ is also negative in the second column model.18 On the other hand, auctioneers would consistently prefer to preselect enterprises that have more past experiences, even though they may not be available due to their resource commitment to something else.

The correlation between the two binary responses seems subtle. It is negative but insignificant. In the following analysis, the second column model is used for inferring _λ_ 1 and _λ_ 2<sup>for Equation (4), because the country and nationality fixed effects are found unignorable;</sup> the chi square test statistic is estimated at 315.36. If this is the case, it mans that there are some unobservables that would facilitate bidders’ entry but discourage auctioneers from qualifying them. Some characteristics shared by new growing companies may be one possibility. While new entrants are eager to enter the market, they may not be trustworthy enough given their past experiences.

> 18 All four measures of project heterogeneity are related to the scale or size of the work. Unsurprisingly, therefore, the estimated coefficients of these variables may be sensitive to specifications. One of the most important independent variables controlling for project heterogeneity may be engineering cost estimates. If the other three variables are omitted from the models, it can be found that the coefficient of the project value is always negative for both equations. The larger a project, the fewer contractors there are who could apply for it. And the larger a project, the fewer applicants there are who are prequalified.
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Table 3. Censored Bivariate Probit Model for Bidders’ Entry and Auctioneer’s Rejection

||Coef.|Std.Err.|Coef.|Std.Err.|
|---|---|---|---|---|
|Equation_d_1|||||
|ln_LENG_|–0.039|(0.092)|0.823|(1.085)|
|ln_LANE_|–0.886|(0.427) <sup>**</sup>|6.679|(2.950) <sup>**</sup>|
|ln_COST_|–0.145|(0.128)|–5.741|(1.815) <sup>***</sup>|
|ln_MONTH_|0.026|(0.312)|27.871|(10.268) <sup>***</sup>|
|ln_BKLG_|0.176|(0.005) <sup>***</sup>|0.010|(0.012)|
|ln_CAID_|–0.084|(0.084)|–26.505|(10.843) <sup>**</sup>|
|Constant|4.805|(0.876) <sup>***</sup>|40.519|(19.833) <sup>**</sup>|
|Equation_d_2|||||
|ln_LENG_|–0.125|(0.106)|–0.782|(0.256) <sup>***</sup>|
|ln_LANE_|0.296|(0.464)|–1.169|(0.669) <sup>*</sup>|
|ln_COST_|–0.188|(0.126)|–0.041|(0.133)|
|ln_MONTH_|–0.250|(0.339)|0.001|(0.601)|
|ln_BKLG_|0.015|(0.014)|0.018|(0.008) <sup>**</sup>|
|ln_CAID_|0.074|(0.088)|1.275|(0.333) <sup>***</sup>|
|Constant|1.140|(1.054)|0.060|(1.773)|
|_ρ_|–0.310|(0.476)|–0.109|(0.374)|
|Obs.|285||285||
|Wald-chi2|1482.66 <sup>*</sup>|<sup>**</sup>|1390.33|<sup>***</sup>|
|No. of country dummies|(0)||(4)||
|No. of bidder nationality dummies|(0)||(5)||
|Chi2 test statistics:|||||
|H0: Coef. of country and bidder|||315.36|<sup>***</sup>|
|nationalitydummies_=_0|||||

Note: The dependent variables are the bidder's entry decisions at individual stages. The robust standard errors are shown in parentheses. *, ** and *** indicate the 10%, 5% and 1% significance levels, respectively.

Source: Author’s calculation.

Finally, the consistent equilibrium bid function is presented in Table 4. The first column model is the simple OLS estimation, which may not be consistent because of uncontrolled selectivity bias. As usually expected, nonetheless, the competition effect is negative, meaning that the equilibrium bid, whence the government procurement cost would decrease with the number of participating bidders.<sup>19</sup> It is also reasonable that the submitted bids would be higher for more valuable contracts, longer highways, and wider roads.

When correcting the possible double selection bias, it is found that the competition effect is still statistically significant but slightly larger (in absolute terms) at –0.707.<sup>20</sup> It means that unrealized bids for some reason would be pro-competitive if they were observable. This can be interpreted as the potential benefits of unrealized competition. The other explanatory variables have the similar coefficients to the OLS regression.

> 19 For more discussion on this static competition effect, see Estache and Iimi (2008a).

> 20 Note that the standard errors were corrected by accommodating the additional disturbance caused by the two bias correction terms; but the coefficient still remains significant.
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The hypothesis that the difference in coefficients between the two models is not systematic cannot be rejected by the standard chi-square test. The test statistic is 2.11 and well below the conventional critical values. Therefore, it can be concluded as follows: There are many prospective bidders, of which bids are not observed, and various factors would likely influence bidders’ entry decision and auctioneer’s qualification decision. Nonetheless, the equilibrium bid function may be able to be estimated effectively through the OLS regression with only observed bids. The competition effect may be slightly underestimated, but the bias will be small.

The estimated bid function reveals another important challenge in procuring infrastructure projects, which is the tradeoff between competition and economies of scale. The bid function exhibits economies of scale; For instance, longer roads are unsurprisingly more expensive, but the unit cost would decrease with the length of roads in a package. The coefficients are well below one (i.e., 0.368 in the OLS case and 0.447 in the double selection model), meaning that a one percent increase in road length would raise the equilibrium bid by only about 0.4–0.5 percent, holding everything else constant. Therefore, auctioneers could save public spending, when they design relatively large procurement packages. However, it will contradict the competition objective; as shown above, a smaller number of applicants could be qualified for longer road projects, and more valuable contracts could also attract fewer bidders.

To highlight the above dilemma between competitiveness and economies of scale, a comparative static analysis is considered. The baseline scenario is evaluated at sample means for explanatory variables. Suppose that the auctioneer downscales the size of contract by 10 percent in terms of engineering cost estimate, leaving everything else unchanged.<sup>21</sup> Then, the probability that a prospective firm decides to apply for the process would increase from 69 to 74 percent (Table 5). This is because more enterprises would be able to accommodate 21 Apparently, it is more natural that some attributes of the project would be changed if the engineering cost is changed. For simplicity, however, the analysis focuses on a simple shock in one single variable.
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smaller works. The probability of an applicant being qualified would also increase 34 to 36 percent, because the auctioneer might be less likely to disqualify bidders for smaller projects. If the predicted probabilities are simply translated into our competitiveness variable _N_ , the degree of competition would increase by 5.2 percent, which would result in 3.7 percent lower bids according to our estimated bid function. This is the benefit from the intensified competition. At the same time, a 10 percent reduction in engineering cost estimates will reduce the bid by 2.3 percent. This is the direct effect of changing the specification of the project. However, recall that the cost estimate was reduced by 10 percent in our scenario. Despite that, the auctioneer is expecting only a 6 percent reduction in predicted bids. As in this scenario, hence, the simple unbundling approach, which aims at dividing a project to a number of small packages, may not always be the solution.

The policy implication is straightforward but challenging. Essentially because potential bidders are resource-constrained, the market competition must of necessity become limited throughout the selection process. If auctioneers divide a project into several small contracts in order to loosen bidders’ resource constraints, the benefit from economies of scale would be sacrificed. These contradictory difficulties could not be solved unless more skilled and competent contractors would emerge and enter in the public procurement markets. In this regard, new entry and local business development, though not achievable in the short term, are of particular importance.

Although it is beyond the scope of this paper, the above discussion may provoke governments to use an alternative approach to procure public contracts, i.e., through negotiation. Theoretically, Bajari and Tadelis (2001) show that more complex transactions would be likely by plagued by ex post adaptations and are better accommodated by a costplus contract, which is opposite to a fixed price contract typically assumed in the auctionbased procurement. Bajari _et al_ . (2006) also provide the supportive evidence of this in the private sector building construction industry. Obviously, however, some important advantages of auctions may have to be sacrificed, e.g., transparency and corruption
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prevention, in addition to competitiveness. These factors may be unignorable in particular in the context of public procurement.

Table 4. Two-Step Estimation for Equilibrium Bid Strategy with Double Selection Process

||OLS|Double<br>selection<br>model|
|---|---|---|
|ln_NUM_|–0.687 <sup>**</sup><br>(0.318)|–0.707 <sup>*</sup><br>(0.368)|
|ln_LENG_|0.368 <sup>***</sup>|0.447 <sup>***</sup>|
||(0.093)|(0.159)|
|ln_LANE_|1.517 <sup>***</sup>|1.621 <sup>***</sup>|
||(0.275)|(0.393)|
|ln_COST_|0.240 <sup>***</sup>|0.226 <sup>**</sup>|
||(0.088)|(0.110)|
|ln_MONTH_|–0.075|–0.108|
||(0.504)|(0.580)|
|_λ_1||0.341<br>(0.274)|
|_λ_2||–0.314|
|||(0.388)|
|Constant|15.054 <sup>***</sup>|15.283 <sup>***</sup>|
||(1.916)|(2.206)|
|Obs.|98|98|
|R-squared|0.939|0.940|
|_F_-statistics|62.77 <sup>***</sup>|56.97 <sup>***</sup>|
|No. of country dummies|(6)|(6)|
|No. of bidder nationality dummies|(8)|(8)|
|_F_test statistics:|||
|H0: Coef. of country and bidder<br>nationalitydummies_=_0|11.85 <sup>***</sup>|9.41 <sup>***</sup>|

Note: The dependent variable is the bidder's entry selection at each stage. The standard errors are shown in parentheses. *, ** and *** indicate the 10%, 5% and 1% significance levels, respectively.

Source: Author’s estimation.

– <u>Table 5. Scenario Analysis An Example</u>

||Baseline<br>|Scenario: 10 percent<br>reduction in<br>engineering cost<br>estimates|
|---|---|---|
|Avg. predicted probability (_d_1_=_1)|68.8|74.1|
|Avg. predicted probability<br>(_d_2_=_1 given_d_1_=_1)|34.4|36.2|
|Predicted bid changes associated with_N_||-3.7|
|Predicted bid chan<br>ges associated with_COST_||-2.3|

Source: Author’s estimation.

# **V. CONCLUSION**

The limited degree of competition is one of the major concerns in infrastructure procurement. The degree of competition that one can observe at the very end of the auction process tends
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to be limited perhaps to about 4–5 bidders. Although one can still expect the conventional competition effect in a static sense, it is important to recall that the entry decision of potential bidders is potentially endogenous. There are a number of prospective bidders, who are interested but may decide not to be involved into the selection process. Hence, the observed distribution of bids will be much different from the distribution of bids that would have been submitted if those potential bidders have participated.

Because of this partial observability, the paper applied the double selection model to procurement data from road development projects in developing countries and examined why some companies did not participate or were not allowed to participate in the bidding process. The estimation results highlight several challenges in infrastructure procurement. Bidders are resource-constrained and self-selective. A few companies can apply for larger road projects. At the same time, auctioneers also tend to limit participation as the contract size increases. They prefer to contract with only experienced contractors. This is the reason the market competition ends up being rather restricted, resulting in high infrastructure procurement costs. The estimated equilibrium bid strategy suggests possible economies of scale; government procurement costs could be saved by increasing the contract size. But it would risk jeopardizing the expected competition effect because, again, larger projects could attract fewer bidders.
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