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Time overruns as opportunistic behavior in public procurement

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Abstract

We consider the supplier’s strategic choice on delivery time in a public procurement setting as the result of the firm’s opportunistic behavior on the optimal investment timing when production costs are uncertain. We model the supplier’s trade-off between the option value to defer the contract execution and the penalty payment in the event of delays. We also take into account the issue of penalty enforcement, which in turn depends on both the discretion of the court of law in voiding contractual clauses and the “efficiency” of the judicial system (i.e. the average length of civil trials). We test our main results on Italian public procurement data showing that the supplier’s incentive to delay is greater the higher the volatility of production costs and the lower the “efficiency” of the judicial system. We then calibrate the model using parameters that mimic the Italian scenario on public works procurement and calculate the maximum amount that a supplier is “willing to pay” (per day) to postpone the delivery date and infringe the contract provisions. Our calibration results are consistent with the theoretical model’s predictions and the empirical findings.

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Notes

  1. Recently, in the same vein, Lewis and Bajari (2011) provided empirical evidence that, when time is an issue, awarding highway procurement contracts through an auction design, scoring the supplier’s bid on costs to execute the contract along with the supplier’s project completion time is more efficient than awarding through an auction where participants bid exclusively on price.

  2. The contract time, starting from when the contract is awarded, can be either specified by the project engineers (Lewis and Bajari 2011, p. 1177), or chosen by the CA aiming at maximizing the total expected welfare function which should account for the gross total value of the project minus the cost of delays (i.e. the value of the project for the taxpayers). In the latter case, without loss of generality, we can assume that the total value of the project is sufficiently high, so that it is always in the interest of the CA to have the infrastructure as soon as possible.

  3. We do not consider the case where the supplier is awarded a premium (incentive) if she delivers the work before the deadline in the contract; this case is scarcely significant in Italy where incentives are very seldom introduced in PPCs due to stringent budget constraints.

  4. Setting the contract time to zero implicitly assumes that the works can be built instantaneously. This assumption can be relaxed without substantially altering the results. Let’s assume that it takes a given “time-to-build” the works but there is a maximum rate, \(m\), at which the supplier can invest in every period (year). Denoting the total expenditure as \(C_{t}\), it takes \(T=C_{t}/m\) periods (years) to complete the project. Assuming that expenditures are made continuously over \(T\), their present value is:

    $$\begin{aligned} \hat{C}_{t}=\int _{0}^{C_{t}/m}me^{-rs}ds=(1-e^{-rC_{t}/m})\frac{m}{r} \end{aligned}$$

    Since \(e^{-rC_{t}/m}\simeq 1-r\frac{C_{t}}{m}+\cdots ,\) we shall have \(\hat{C}_{t}\simeq C_{t}\) and the analysis can similarly proceed as in the text.

  5. In (2), \(dz_{t}\) is the increment of a standard Brownian process with mean zero and variance \(dt\) (Dixit and Pindyck 1994).

  6. Assuming that the state variable follows a Geometrical Brownian Motion is standard in real-option models. However, alternative processes such as mean-reverting, can be used. This would complicate the analysis, without changing the results significantly.

  7. This assumption, which allows us to find closed-form solutions, is rather unrealistic, since the CA is generally entitled to terminate the contract when delays become “unacceptably long” . For example, Italian law caps the maximum amount of the penalty to be paid by the supplier at 10 % of \(p\) (see art. 145 Presidential Decree no. 270/2010). If the delays incur a penalty exceeding this threshold, the CA can terminate the contract and award the works to another supplier. In this case (3) becomes an American Put Option, with a maturity time \(T\) given by: \(\int _{0}^{T}ce^{-rs}ds=10~\%p.\) Modeling this option is more complicated than (3), but none of the results presented in this section are substantially affected.

  8. The solution to \(E_{t}(e^{-r(\tau -t)})\) can be obtained by using dynamic programming (see, for example, Dixit et al. 1999). Since \(F_{t}\) is driven by a Geometric Brownian Motion, the expected discount factor is increasing in \(F_{t}\) and decreasing in \(F_{\tau }\); then it can be defined by a function \(\Lambda (F_{t};F_{\tau })\). Over the infinitesimal time interval \(t+dt,\, F_{t}\) will change by the small value \(dF_{t},\) hence we get the following Bellman equation: \(r\Lambda (F_{t};F_{\tau })dt=E(d\Lambda (F_{t};F_{\tau })).\) By applying Itô’s Lemma to \(d\Lambda \) we obtain the following differential equation:

    $$\begin{aligned} \frac{1}{2}\sigma ^{2}F_{t}^{2}\Lambda ^{\prime \prime }+\alpha F_{t}\Lambda ^{\prime }-r\Lambda =0\,, \end{aligned}$$

    which can be solved by imposing the two boundary conditions: \( \lim _{F_{t}\rightarrow \infty }\Lambda (F_{t};F_{\tau })=0\) and \( \lim _{F_{t}\rightarrow F_{\tau }}\Lambda (F_{t};F_{\tau }))=1.\) The general solution is \(\Lambda (F_{t};F_{\tau }))=\left( \frac{F_{t}-1}{F_{\tau }-1} \right) ^{\beta },\) where \(\beta <0\) is the negative root of the auxiliary quadratic equation \(\Psi (\beta )=\frac{1}{2}\sigma ^{2}\beta (\beta -1)+\alpha \beta -r=0.\)

  9. The first order condition is:

    $$\begin{aligned} \frac{\partial P}{\partial F_{\tau }}&= \beta \left( \frac{F_{t}-1}{F_{\tau }-1}\right) ^{\beta -1}\left( -\frac{F_{t}-1}{(F_{\tau }-1)^{2}}\right) \left( F_{\tau }+\pi \frac{c}{r}\right) +\left( \frac{F_{t}-1}{F_{\tau }-1}\right) ^{\beta } \\&= \left( \frac{F_{t}-1}{F_{\tau }-1}\right) ^{\beta }\left[ \beta \left( -\frac{1}{F_{\tau }-1}\right) \left( F_{\tau }+\pi \frac{c}{r}\right) +1\right] =0 \end{aligned}$$

  10. For further details on the descriptive analysis we run on the AVCP’s database, see D’Alpaos et al. (2009).

  11. Similar empirical evidence on the delivery delays in Italian public procurement contracts has been provided—with different data extensions—by Guccio et al. (2009), Bucciol et al. (2013), Coviello et al. (2013), Decarolis (2013).

  12. In Italy, before the Governmental Decree no. 163/2006, PPCs were regulated by Law no. 109/1994 and Presidential Decree no. 554/1999, which defined the main awarding procedures as: “pubblico incanto”, “licitazione privata”, “licitazione privata semplificata” and “trattativa privata” . The “pubblico incanto” is an open procedure in which any firm certified as being qualified to do the works involved can participate. The “licitazione privata” and “licitazione privata semplificata” are similar to the “pubblico incanto” except that participants are invited by the CA providing they satisfy certain technical characteristics. The “trattativa privata” is a private negotiation where the CA invites a limited number of participants (minimum 15). The AVCP dataset records the awarding procedures in accordance with legislation applicable at the time (between 2000 and 2006 in our case). We grouped the data into two main awarding procedure groupings: i.e. “open” and “negotiated” procedures. In our regression analysis we created a dummy variable where the open procedure equates to 1.

  13. Among the various types of Italian CA, we considered: Public Administrations, Regional Authorities, Territorial Associations in Mountain Regions, Provincial Authorities, Municipalities, the National Health Service, National Railways, National Roadworks Board (Anas), Postal Services, public corporations and other public organizations, concessionaires and administrators of public infrastructures and networks, and the Council Housing Board (IACP).

  14. The geographical distinction into macro-regions has been made referring to the definition provided by the Italian National Institute of Statistics (ISTAT) which divides Italy into three macro-regions: 1) Northern Italy (which comprises Piedmont, Valle d’Aosta, Liguria, Lombardy, Trentino Alto Adige, Veneto, Friuli-Venezia Giulia, Emilia Romagna); 2) Central Italy (which includes Tuscany, Umbria, Marche and Lazio); 3) Southern Italy (which is composed of Abruzzo, Molise, Campania, Puglia, Basilicata, Calabria, Sicily and Sardinia).

  15. Jappelli et al. (2005) theoretically showed that judicial efficiency affects credit constraints and increases lending; they test their model finding that in Italian provinces with longer trials—or with large backlogs of pending trials—credit is less widely available. Coviello et al. (2013) showed that the CA’s high legal cost to defeat the firm’s claim on penalty enforcement can determine an equilibrium where the firm delays and the CA does not enforce the penalty; they test their model on a sample of Italian public procurement contracts similar to the one analysed in this paper and find a robustpositive relationship between the province’s average duration of civil trials and the contract’s delay in execution. Note that their empirical strategy and model specification are different from those presented here: in particular, they include a larger number of controls (both at contract and local levels) and robustness checks to exclude the influence of competing socio-institutional determinants of delays in the contract delivery (e.g. corruption, CA’s budget hardness from the local stability and growth pact).

  16. For the sake of clarity it should be pointed out that the empirical model is not a direct estimate of the theoretical model but rather an attempt to verify the model’s theoretical predictions.

  17. The CA production costs estimate is calculated by engineers from the bill of quantities (i.e. a document containing an analytical and detailed statement of the different items of the works, labor and materials, including a contingency sum, involved in a proposed public works). This estimate is used to establish the reserve value in the contract awarding procedure and as a benchmark to assess the bids submitted and identify abnormally low bids (see Italian Governmental Decree no. 163/2006).

  18. See De Silva et al. (2008) for a discussion on the common cost component.

  19. In our regression, we found that COV and CVA are positive, and since they might be both affected by the option value (even if COV might be affected by the option value, CVA by its variability), we checked for collinearity. All the tests (tolerance, VIF and collinearity diagnostics) confirmed the absence of collinearity in our regression (these tests are available on request). A possible explanation for this absence of collinearity might be that COV captures the dimension of the project (larger works implying longer delays), while CVA captures the option value (higher cost variability meaning longer delays).

  20. The regressions in Tables 2 and 3 were completed with SPSS software: the same results emerged by using Stata software, but in this latter case, the standard errors were clustered by regions.

  21. PRO is significant in regressions 1, 2 and 4, but it is not in regression 3. It also has a sign that is sometimes positive and sometimes negative. In particular, when we discard the province fixed effect, the significance of PRO is null. This may be because the province is an important variable and ruling it out generates an omitted variable bias, making the estimate unreliable.

  22. Comparing the four regressions, we see that R\(^{2}\) decreases when we do not control for the province fixed effect, while it is similar in the other cases: this suggests that local conditions significantly affect the execution time.

  23. Note that, when we estimate (7) for each range value, by construction, there is no variation in CVA among projects within the same cost category and the same year, but, since the dataset extends for 7 years, there exists variability within the 7-year period for each sub-group.

  24. This is also consistent with some recent theoretical and empirical contributions on procurement auctions. Goeree and Offerman (2003) demonstrated that bidding competition is more aggressive in auctions with larger common cost uncertainty and Dosi and Moretto (2012) show that an option value to delay the execution of a project can be generated by the uncertainty over the common component of the construction costs. De Silva et al. (2008) empirically showed a marked decline in the value of bids for highway procurement auctions when the common uncertainty about the costs was great and the CA’s internal estimate of the project cost was revealed to all bidders.

  25. We performed a Chow test I for the contract value range, obtaining an F test result of 112 and a p-value of 0.000, and a Chow test II for the contract value range, obtaining an F test of 15.72 and a p-value of 0.000.

  26. Bajari and Tadelis (2006) use the term “simple” to denote a project which is “easy to design with little uncertainty about what needs to be produced” (p. 124).

  27. This discretionality of the court is commonly referred to as the “liquidated damages principle” (DiMatteo 2001). Delay in delivering the contracted investment should be referred to a specific case of the supplier’s breach of contract, and the court can apply the above principle to cover the reasonable damages caused to society by delays. For a discussion of the application of the “liquidated damages principle” in PPCs, see Dimitri et al. (2006, Ch. 4, pp. 85–86); for an analysis of the economic incentives pertaining to it, see Anderlini et al. (2007).

  28. In the US experience of PPCs in the highway construction industry, the “unit time value” is typically expressed as a cost per day. It is calculated by the State Highway Agency referring to the “daily road-user cost”, which includes items such as travel time, travel distance, fuel expense, etc. See Herbsman et al. (1995) for an example of the “daily road-user cost” calculated by the Kansas Department of Transportation.

  29. Italian legislation sets maximum and minimum penalties for the inclusion in PPCs. Specifically, the per day penalty can range from 0.03 to 0.1 % of the contract price. See Governmental Decree no. 163/2006 and Presidential Decree no. 270/2010. See in particular art. 145 Presidential Decree no. 270/2010.

  30. Although \(r\) should be the return that an investor can earn on other investments with comparable risk characteristics, throughout our analysis we simply refer it to the social discount rate recommended by the Italian Government in assessing public projects. This rate ranges between 8 % and 12 %, possibly dropping to 5 % for projects undertaken in the south of the country (see Pennisi and Scandizzo 2003).

  31. To emphasize the effect of the contract’s profitability on the supplier’s decision concerning the delivery date, we fix the mark-up at 30, 20 and 10 %.

  32. \(\alpha =2.5{-}3~\%\) is the average trend of the increase in costs for public infrastructure and residential buildings from 1996 to 2006. The data used to estimate this trend were provided by ISTAT.

  33. Simulations were conducted also ceteris paribus for \(\eta =0.5\) and for \(r\) =10 %. Results are available on request to the authors.

  34. Note that all the results according to which the CA finds it convenient to set the penalty as equal to \(\underline{c}\) are bolditalicized in the tables.

  35. For a more extensive analysis on the length of civil trials in Italy see D’Alpaos et al. (2009).

  36. We set \(\alpha =0\) to neutralize the effects of inflation and to focus only on regional effects.

  37. These findings are confirmed, ceteris paribus, for \(\eta =0.3\) where \( c^{*}=0.11~\%\) in NCI while \(c^{*}=0.22~\%\) in SI. Results are available on request to the authors.

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Acknowledgments

We would like to thank M. Bigoni, C. Dosi, P. Garella, G. Marella, A. Meggiolaro, R. Miniaci, L. Moretti, I. Macho Stadler, G. Neri, P. Piacentini, H. Paarsh, D. Perez Castrillo, G. Spagnolo, T. Valletti, L. Zanettini, G. Zwart, the seminar participants at the SFB-TR15 Berlin Seminar Series, at the 2012 workshop “The Economics of Irreversible Choices”—Univ. of Brescia, at the 2009 workshop on Industrial Organization—Univ. of Salento, at the 2007 Cofin workshop—Univ. of Padua, at EAERE 2009, at EARIE 2008, at EEA 2008, for very useful comments and suggestions. We are also grateful to the Osservatorio dell’ Autorità per la Vigilanza sui Contratti Pubblici di Lavori, Servizi e Forniture (AVCP) for the dataset provided. We acknowledge the financial support by the Italian Ministry of Education (MIUR), projects 2006130472_003 and 20089PYFHY_002. The usual disclaimer applies.

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Authors and Affiliations

  1. Department of Civil, Environmental and Architectural Engineering, University of Padua, via Venezia, 1, 35131 , Padova, Italy

    Chiara D’Alpaos

  2. Department of Economics and Management, University of Padua, Fondazione Eni Enrico Mattei and Centro Studi Levi-Cases, Via del Santo, 33, 35123 , Padova, Italy

    Michele Moretto

  3. Department of Economics and Management, University of Padua, Via del Santo, 33, 35123 , Padova, Italy

    Paola Valbonesi

  4. Department of Economics and Management, University of Brescia, Fondazione Eni Enrico Mattei, Via San Faustino, 74/b, 25122 , Brescia, Italy

    Sergio Vergalli

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  1. Chiara D’Alpaos
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  4. Sergio Vergalli
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Correspondence to Sergio Vergalli.

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D’Alpaos, C., Moretto, M., Valbonesi, P. et al. Time overruns as opportunistic behavior in public procurement. J Econ 110, 25–43 (2013). https://doi.org/10.1007/s00712-013-0352-6

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