Political Contestability and Contract Rigidity:An Analysis of Procurement Contracts

Jean Beuve∗

Marian Moszoro†

Stéphane Saussier‡

June 7, 2014

Abstract

We compare procurement contracts where the procurer is either a public agentor a private corporation. Using algorithmic data reading and textual analysis ona rich dataset of contracts for standardized a product and services from a singleprovider, we find that public contracts feature more rigidity clauses, and theirrenegotiation is formalized more frequently in amendments than private-to-privatecontracts. We further compare in-sample public contracts and find similar patternsrising in political contestability by several measures. We argue that a significantpart of contractual rigidity difference between purely private and public contractsis a political risk adaptation of the public agent to curtail plausible challenges frompolitical contesters and interest groups.

Keywords: Contractual Rigidity, Renegotiation, Political Contestability, Privateand Public Procurement.

∗CES-University of Paris 1 Panthéon Sorbonne†University of California, Berkeley and Kozminski University‡IAE-Sorbonne Business School

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1 Introduction

In this paper, we build on Spiller [2008] and Moszoro and Spiller [2012, 2014], argu-ing that public–private contracts are characterized by intrinsic differences coming fromthird-party opportunism that affect them, i.e., a substantial amount of supervision andcontrol is done by third parties such as political contesters and interest groups). Afundamental difference between private and public contracts is that public contractsare in the public sphere, and thus, although politics is normally not necessary to under-stand private contracting, it becomes fundamental to understanding public contracting.This makes a big difference with private contracting: when faced with unforeseen orunexpected circumstances, private parties, as long as the relation remains worthwhile,adjust their required performance without the need for costly and formal renegotiation(i.e., relational contracting (Baker et al. [2002])). Public contracting, on the other hand,because of potential hazards posted by interested third parties, is characterized by for-malized, standardized, bureaucratic, rigid procedures, partly because politics need to besecured against third-party opportunism (TPO hereafter). This effect is reinforced bythe risk of government opportunism leading private parties pushing for rigid contracts(Moszoro and Spiller [2014]). Building on this, we derived two testable propositions.First, public contracts should be more rigid compared to equivalent transactions gov-erned under private contracting. This is a direct consequence of intrinsic characteristicsof public contracting. Second, contracts signed with public authorities that are moreprobably challenged by third parties (i.e., more politically contestable) will be charac-terized by more rigid procedures compared to other public contracts. This is becausepublic authorities that may be challenged want to secure even more contractual agree-ments. One consequence is that public contracts should be more frequently renegotiatedbecause of their initial rigidity and the willingness of public contracting parties to adaptthe contract through formal amendments (i.e., no relational adaptation).

In order to test these two propositions we collected unique data and used a cutting-edge methodology. Our data concern car park contracts, signed between 1963 and 2009in France. In our dataset, we analyze 436 contracts and more than 850 amendments,signed between one private operator and 26 private procurers or between this sameprivate operator and 152 public authorities. In addition, we also collected data on localelections and we propose several measures of political contestability. Because there isonly one contractor and car parks arguably entail standardized a product and services,a large part of the heterogeneity comes from the procurers’ characteristics and time-varying political contestability. Following Schwartz and Watson [2012] characterizationof rigid contracts and using algorithmic data reading and textual analysis on this richdataset of contracts, we find that public–private contracts feature more rigidity clausesand their renegotiation is formalized in amendments. We further compare in-samplepublic contracts and we find similar patterns rising in political contestability by severalmeasures. We argue that a significant part of contractual rigidity difference between

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purely private and public contracts is a signaling device and political risk adaptationof the public agent to curtail plausible challenges from political contesters and interestgroups. We also find, as expected, that public contract are more frequently renegotiated.

Our study contributes to contract theory in advancing a novel set of propositionsbased on third-party hazards faced by public, but not by private procurers. Our resultssuggest that some previous empirical studies that pointed out to contractual inefficien-cies of public–private contracts due to high renegotiation rates (Guasch [2004]; Guaschet al. [2008]) might be partly misleading. Frequent renegotiations observed in public pri-vate contracts (Guasch [2004]; Beuve et al. [2014]) can be understood as the consequenceof the specific nature of public contracts instead of the manifestation of opportunism:“In a sense, it is possible to say that the frequency of contract renegotiation may pro-vide concessions a relational quality” (Spiller [2008], p. 22). One important corollary isthat the perceived inefficiency of public contracting is largely the result of contractualadaptation to different inherent hazards, and as such is not directly remediable.

The paper is organized as follow. In section 2. we come back on the specificitiesof public contracting and what Spiller [2008] paper calls third-party opportunism. Wederive propositions concerning rigidity and political contestability of public contracts.In section 3, we present our data and our empirical strategy to put our propositions tothe test. Section 4 is dedicated to the results. In section 5, we discuss our results andwe propose several robustness checks. Section 6 concludes.

2 Third-Party Opportunism and the Rigidity of PublicContracts

2.1 The Inefficiency of Public Contracts

2.1.1 Public–Private Contracts and Renegotiations

Because they deal with services of general interest, public–private contracts are scru-tinized especially closely by researchers. One striking empirical evidence is the factthat very often, public contracts are renegotiated. Many examples of renegotiations inpublic–private agreements are provided by Guasch [2004]. By studying more than 1,000concession contracts signed in Latin American countries between the mid-1980s and2000, he found that 78% of transportation contracts and 92% of water and sanitationcontracts were renegotiated. The authors findings also confirmed that renegotiationsoccur shortly after the award (on average, 2.2 years) and often, at first glance, favor theprivate party. Guasch [2004] suggests that renegotiations are a consequence of aggres-sive bids in the context of an ex ante lack of commitment from the government. Becausethe government is unable to commit not to renegotiate and because firms only learntheir types after bidding, if a firm wins a call for tenders and discovers it is inefficient(i.e., it would lead to losses), it will be tempted to renegotiate (Laffont [2003]; Guaschand Straub [2006]; Guasch et al. [2008]).

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Other researchers explore alternative explanations such as government-led renego-tiations (Guasch et al. [2007]), as well as renegotiations without hold-up that enableincumbent governments to circumvent budgetary rules before elections (Engel et al.[2009a]). As stated by Guasch et al. [2008, p. 421], “such high rates of contract rene-gotiation have raised serious questions about the viability of the concession model indeveloping countries”.

It is fair, however, to recognize that high rates of renegotiation are not specific toless developed countries. Other studies pointed out very high renegotiation rates in theUnited Kingdom (NAO [2003]), United States (Engel et al. [2011]), and France (Athiasand Saussier [2007]; Beuve et al. [2014]). Whatever the theoretical framework mobilizedin order to analyze contractual issues at stake in public–private contracts, the high rateof renegotiations always come as bad news.

2.1.2 Contractual issues

Following Oliver Williamson’s canonical paper on franchise bidding (Williamson [1976])pointing out contractual failures at different stages (i.e., selection, execution, and re-newal stage), many recent papers study public–private contracting issues, such as thequestion of competition vs. negotiation at the selection stage (Bajari et al. [2011,2009]; Lalive and Schmutzler [2011]; Vellez [2011]; Chever and Moore [2012]; Amaralet al. [2013]), collusion and corruption (Compte et al. [2005]; Martimort and Straub[2006]), contract enforcement and renegotiations at the execution stage (Engel et al.[2009b]; Gagnepain et al. [2013]; Guasch et al. [2007, 2008]; Chong et al. [2014]), aswell as contract renewals (Beuve et al. [2014]). Those studies build on several theoret-ical frameworks that emphasize asymmetric information, incomplete contracting, andtransaction costs problems.

On the one hand, the agency theory focuses on incentives issues arising from asym-metric information. However, as stated by Malin and Martimort [2000] and followingSappington and Stiglitz [1987]’s irrelevance theorem, “incentive theory has nothing tosay about such things as the distribution of authority within an organization, the limitsof the firm, the separation between the public and the private spheres of the economy,and more generally nothing to say about organizational forms and designs” (Malin andMartimort [2000], p. 127-128). In order for this theory to be able to add something tothose issues, incentive models must take into account various forms of transaction coststhat lead to contract incompletenesses which can be easily described.

This can be done by adding ad hoc assumptions such as limited commitment of thegovernment. One very nice example is given by (Guasch et al. [2008]) who stress govern-ment failure to commit not to renegotiate. On the other hand, the incomplete contracttheory (Hart et al. [1997]) postulates that contracts are incomplete and always rene-gotiated, leading to inefficiencies (i.e., renegotiation is efficient but because it concernsthe surplus net of initial investments, it leads to hold-up).

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The transaction cost theory proposes a middle-way position, stating that contractsare incomplete, and views renegotiations as a costly but necessary process, suggestingthat there exists an optimal level of contract completeness and thus an optimal levelof renegotiation (Crocker and Reynolds [1993]; Masten and Saussier [2000]; Saussier[2000]). Whatever the theoretical frameworks considered, very few is incorporated inorder to take care of the specific nature, if any, of public contracting compared to privatecontracting.

An exception are Spiller [2008] and Moszoro and Spiller [2014], which insist on thespecific nature of public private contracts leading to a more nuanced interpretation ofrenegotiation rates observed in public contracts.

2.1.3 The Specific Nature of Public–Private Contracts

As stated by Spiller [2008], a fundamental difference between private and public con-tracts is that public contracts are in the public sphere. Politics, that is normally notnecessary to understand private contracting, becomes fundamental to understandingpublic contracting. A consequence of this is that third-party opportunism prevents theuse of relational contracts for public–private contracts. Third-party opportunism refersto the fact that public contracts are subject to public scrutiny in order to avoid corrup-tion and graft. This scrutiny is undertaken by designated agencies in charge of contractsupervision. Furthermore, supervision is also done by interested third parties that maybehave opportunistically and challenge the “probity” of a public agent. This is notspecific to public contracting. However, even in the face of third-party opportunism,companies normally rely on inter-firm relationships to support contracting (Macaulay[1963]), through informal and continuous adaptations.1 The exposure to third-partyopportunism increases the risk to both the public agent and the private party. In re-sponse, both will have incentives to increase the rigidity of these contracts as comparedto equivalent contracts between private parties. That is why, because of their nature,public contracts are born with less flexibility than normal private contracts (Spiller[2008], page 21).

2.2 Public Contract Rigidity: propositions

Building on Spiller [2008]’s view of public contracting, it is easy to make some propo-sitions concerning the features of public contracts. Contracting cost rises exponentiallyin contract rigidity and determines the trade-off between interpretation accuracy andcost of contract writing, as shown by Schwartz and Watson [2012]. In Moszoro andSpiller [2012], the lack of flexibility in public procurement design and implementationreflects public agents’ political risk adaptation to limit hazards from opportunistic third

1Relational contracts are defined as informal commitments governing non-contractible actions andsustained by the value of future transactions (Bull [1987]; Baker et al. [2002]). When the discountedpayoff stream from commitment to this informal agreement is higher than the discounted payoff streamfrom deviation, a relational contract is sustainable and allows to avoid ex post opportunism.

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parties—political opponents, competitors, interest groups—while externalizing the asso-ciated adaptation costs to the public at large. Public agents minimize both contractingand political costs given by:

minimizeR

Φ = T0 ρ(R)τ(R) +K(R) (1)

where K(R) are adaptation costs rising exponentially in contract rigidity, ρ is the like-lihood of a challenge by an opportunistic third party and τ is the likelihood of successof an opportunistic challenge, both decreasing in contract rigidity, and T0 is the publicagent’s (political) cost if a challenge by third parties is successful.

Third parties observe benefits from opportunistic challenge, but the public agentdoes not know ex ante the particular value of these benefits for third parties. Thirdparties’ overall benefits from an opportunistic challenge correspond to a random nor-mally distributed variable T̃0. Equation (2) shows that in equilibrium third partieschallenge a contract only if expected gains T̃0ζτ are bigger than litigation costs c(R):

ρ ≡ Pr[T̃0ζτ(R) > c(R)], (2)

where ζ ∈ [0, 1] is a political concentration parameter; if ζ = 1, the TPO challenger’sbenefits are symmetrical to the incumbent public agent’s TPO costs (e.g. a bipartisanpolitical market); if ζ < 1, the political market is fragmented and the challenger doesnot internalize all benefits from a successful contract protest.

Litigation costs c(R) rise in R. Reduced flexibility limits the likelihood of oppor-tunistic challenge lowering third parties’ expected gains and increasing litigation costs.Any deviation from equilibrium rigidity R∗ makes the public agent worse off:

1. If R < R∗, then τ(R) > τ(R∗), c(R) < c(R∗), therefore ρ > ρ∗ and T0 ρ(R)τ(R)−T0 ρ(R∗)τ(R∗) > K(R∗)−K(R) (political cost increase offsets gains in contractingcost decrease)

2. If R > R∗, then T0 ρ(R∗)τ(R∗)−T0 ρ(R)τ(R) < K(R)−K(R∗) (contracting costincrease outmatches gains in political cost decrease)

Moszoro and Spiller [2012] model yields two testable predictions on the contractualdesign depending on the characteristics of the contracting parties:

Proposition 1. In the absence of political costs, equilibrium contract rigidity is lowerthan when political costs are high, therefore contracts subject to public scrutiny showmore rigidity clauses than purely private relational contracts;

Proposition 2. In contestable political markets (high ζ), contracts show more rigidityclauses than in monopolized or atomized political markets (low ζ).

A direct consequence is that public contracts are more probably renegotiated thanprivate contracts in order to adapt to unforeseen contingencies.

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Figure 1: Propositions

3 Empirical Analysis

3.1 Sector and Contracts Characteristics

In many European countries, cities are responsible for the provision of on-street and off-street car parks. The positive externalities and social benefits (environmental concerns,intermodality, urban development, etc.) derived from a high quality of constructionand efficient management of car parks are the reasons why they are under the remit oflocal authorities. However, although the public authorities must retain the ownershipand control of car parks, they can outsource the provision of such infrastructure andservices through public–private arrangements. In France, as in many other countries,outsourcing car parks construction and/or management to private operators has beenwidespread.2 As a consequence, the sector is characterized by a strong competition be-tween national and international companies3 as well as local firms (Baffray and Gattet[2009]). The competitive pressure also comes from the possibility for municipalities toreturn to in-house provision when contracts end. The sector is characterized by the ex-istence of three main contractual arrangements, namely “concession”, “operating” and“provision of services” contracts.

Concession Contracts. When the park has to be built or when important investments are2According to the French Ministry of Sustainable Development, in 2009 73% of car parks are orga-

nized via outsourced management and 27% provided in-house through public provision.3Vinci Park, Q-Park, Epolia, Efia, Interparking, Parking de France, UrbisPark, AutoCité and SAGS

are the most frequent bidders in France.

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necessary to renovate the infrastructure, municipalities use concession contracts. Theseare long-term contracts (30 years in average in our dataset) which provide sufficient timefor private operators to invest as well as to pay off the debt. In such contracts, the oper-ator bears the demand risk and is remunerated with user fees. The direct consequenceis that long-run contracts are subject to the political, economic, social and technicalchanges that may occur during the execution of the contract. Such changes may beexogenous to the contract (technological developments, economic shocks, changes inlegislation or legal interpretation) or may directly result from internal drivers (evolvingbusiness requirements) or contract maladaptations (inappropriate initial contractual de-sign). Such changes may then involve adaptations to the service.

Operating Contracts. When the car park is already built and requires major or in-termediate level of investment to renovate and to maintain it, operating contracts areused. These are shorter contracts than concession contracts (18.2 years in average inour dataset). As for concession contracts, the operator bears the demand risk and isremunerated with user fees. Likewise, operating contracts are subject to the political,economic, social and technical changes that may occur during the execution of the con-tract.

Provision of Services Contracts. When the car park is already built and requires noinvestments to renovate it and for on-street car parks, provision of services contractsare used. These are shorter contracts (3.2 years in average in our dataset).

3.2 Contractual and Political Data

In the French car parking sector, data are not centralized because of the lack of aregulatory authority. Therefore, in order to generate the dataset used in this study,we examined all contracts signed by the leader company of the french market (42%market share among private operators; 30.6% total market share) between 1963 and2009. Overall, we assessed 436 contracts and 857 amendments to contracts with 152public authorities dispersed in 59 different departments (out of 96) in metropolitanFrance.

Concerning political data, we gathered the outcome of all municipal elections from1983 to 2008.4 Elections are organized (in principle) every six years to elect the mayorand the members of the city council by a majority vote spread over two rounds (directuniversal suffrage). Each mayoral candidate has to present a list of potential deputies(as many deputies as number of seats at the city council). The list which obtains thehigher result obtains 50% of the seats at the city council. The remaining seats aredistributed among all lists (including the majority list) who received at least 5% of

41983, 1989, 1995, 2001 and 2008

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the votes cast. The city council, chaired by the mayor, has collectively the legislativeauthority on the municipal territory. More precisely, the council has a general matterjurisdiction to manage the affairs of the municipality through its decisions. Hence, thecity council approves the budget prepared by the mayor and his deputies, determineslocal tax rates, creates and cancels communal jobs, allows acquisitions and disposals ofcommunal property, approves loans, and grants subsidies and sets tariffs for communalservices and on-street car parks.

3.3 Empirical Strategy

3.3.1 Explained Variable

In order to assess the rigidity level of our contracts we relied on Schwartz and Watson[2012] and we introduce rigidity categories—arbitration, certification, evaluation, litiga-tion, penalties, contingencies, design, and termination—and construct “dictionaries” bywhich we machine-read contractual dimensions.5 These rigidity categories capture rele-vant contractual clauses that lower the likelihood of a challenge by opportunistic thirdparties, and are orthogonal to designative specifications that would preclude a competi-tive market. Our rationale for (and contribution to) the use of rigidity categories insteadof the simple aggregate is to open the black box on contractual rigidity and assess themagnitude and significance at a granular level. We counted 34,681 keywords overall:Arbitration 10,241; Certification 3,263; Evaluation 8,090; Litigation 2,479; Penalties5,431; Contingencies 4,488; Design 109, and Termination 580. We created as manyvariables as rigidity dimensions. Table 1 presents keywords clustered in eight rigiditycategories.6 and Figure 2 presents the mean score obtained by private and public con-tracts on each rigidity dimension. We clearly see that, on average, public contractsare more rigid than public ones, whatever the dimension considered at the exception ofDesign.7

In a multidimensional setting where each category is a dimension, the degree ofdifference between contracts can be measures by the (a) cartesian distance betweenthe points given by the vectors of word categories, (b) the difference in the angle of thevectors of word categories, and/or (c) the difference in frequencies of word categories. In

5See, for example, Parkhe [1993] for an application of categories for the analysis of contracts in themanagement literature and Loughran and McDonald [2011, 2014] for the analysis of corporate filingsin the finance and accounting literature. Parkhe uses dummy variables for periodic written reports ofrelevant transactions, prompt written notice of departures from the agreement, the right to examineand audit relevant records through a firm of CPAs, designation of certain information as proprietaryand subject to confidentiality provisions of the contract non-use of proprietary information even aftertermination of agreement, termination of agreement, arbitration clauses, and lawsuit provisions in asmall contract sample. Loughran and McDonald use word count of negative words, positive words,uncertainty words, litigious words, strong modal words, and weak modal words in large number of SECfilings.

6Plurals (e.g. penalties) and variations (e.g. penalized) are also counted.7The fact that Design is not relevant reinforces our argument: too specific design could indicate

“designative specifications,” i.e., point to a specific contractor and be the source of favoritism Lambert-Mogiliansky and Kosenok [2009].

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the present study, we use the normalized frequencies of word categories (i.e., z-values).For instance, we transformed the word counting result of Arbitration by calculating:

zArbitration = Arbitration− µσ

(3)

where µ is the mean and σ is the standard deviation of count of Arbitration. This givesus a global rigidity measure zRigidity:

zRigidity = zArbitration+ zCertification+ zEvaluation+ zLitigation

+zPenalties+ zTermination+ zContingencies+ zDesign(4)

Table 1: Keywords searched and grouped into contract rigidity categories

Arbitration appeal, arbitration, conciliation, guarantee, intervention,mediation, settlement, warrantly, whereas

Certification certification, permit, regulation

Evaluation accountability, control, covenant, obligation,quality, specification, scrutiny

Litigation court, dispute, indictment, jury, lawsuit, litigation,pleading, prosecution, trial

Penalties damage, fine, indemnification, penalty, sanction

Termination breach, cancel, dissolution, separation, termination, unilateral

Contingencies contingent, if, provided that, providing that, subject to,whenever, whether

Design anticipation, event, scenario, plan

3.3.2 Public vs. Private Contracts

We created a dummy variable Public that equals 1 when the contract is signed betweenthe operator and a municipality and 0 when the contract is signed with a private partner(e.g., a private company or shopping center).

3.3.3 Political Contestability

The first variable we define, HHIm,t, is the Herfindahl-Hirschman Index of the firstround of elections preceding the date of signature:

HHIm,t = A2m,t +B2

m,t + C2m,t +D2

m,t + . . . (5)

where Am,t is the winning party’s vote share in municipality m at time t, Bm,t is therunner-up party’s vote share, Cm,t is the vote share of the party who came in third

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place, etc. According to our Proposition 2, we expect that politically concentratedmunicipality should lead to less rigid contract.

The second variable we propose allows to capture the opposition force to the winningparty. Thus, we take into account the number of different lists (Number_Of_Listsm,t)which applied to first round of elections and the concentration of all non-winning parties(Residual_HHIm,t) in municipalitym at time t which measure the strength of politicalopposition:

Residual_HHIm,t =

(B2

m,t + C2m,t +D2

m,t + . . .)

(1−Am,t)2 (6)

We expect here that the stronger the political opposition, the more rigid the contract.Those two variables thus might have a positive impact on contractual rigidity.

The third variable is the simple margin of victory (Win_Marginm,t) between thewinning and the runner-up party. We also introduce a square term of the variable toidentify a potential non-linear effect (Win_Margin2

m,t)

Win_Marginm,t = Am,t −Bm,t (7)

Win_Margin2m,t = (Am,t −Bm,t)2 (8)

As for the variable HHIm,t, we expect that the larger the win margin, the less rigid thecontract.

The fourth variable, Distancem,t, corresponds to the distance between the date ofsignature of the contract and the date of the future election. This variable simultane-ously captures the closeness of the next elections and the mayor tenure in office in thepolitical cycle. The intuition here is that we may have more rigid contracts closer toupcoming election years. This would be evidence of opportunistic behavior from thepublic agents.

The fifth and last variable accounts for political swings during the last three electionspreceding the date of signature:

Swingsm,t =3∑

t=1PartyChangem,t (9)

where PartyChange is a dummy variable equaling one if a mayor’s seat changes partyhands in municipality m at time t. As a change in political majority can be interpretedas a sign of higher political contestability, we might observe a negative impact of ourvariable Swingsm,t on contract rigidity.

3.3.4 Control Variables

Aside from the nature of the contract (public vs. private) and the level of politicalcontestability, other factors can be mobilized to explain contractual rigidity. As a con-sequence, we include a set of control variables. First, we take into acocunt the three

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different types of contract described in section 3.1 through three dummy variables:Concessioni,t, Operatingi,t and Provision_of _Servicesi,t. In the estimations, conces-sion and provision of services contracts are compared to operating contracts. As thosecontractual arrangements correspond to different levels of investments and complexity,we should observe that concession contracts are more rigid than operating contracts,and operating contracts are more rigid than provision of services contracts.

We also introduce variables controlling for the size of the city concerned by thecontract (measured through the number of inhabitants, Inhabitants), the political colorof the mayor (Left_Wing vs. Right_Wing), as well as the fact whether the consideredcontract is a renewed contract (Renewed). Finally, as the estimation results could bedriven by unobserved characteristics, we control for potential biases by introducing thevariable Trend that stands for the year of signature of contract, and by adding yearand geographical areas (Department) dummies in order to capture fixed effects linkedto where and when contracts have been signed. Descriptive statistics of all the variablesused in the empirical strategy are provided in Table 2.

3.3.5 Identification Strategy

Our goal is to explore how public and private contract differ concerning their level ofrigidity. In order to do so, we estimate the following model:

zRigidityi,t = Publici,tγ +Xi,tα+ Yi,tβ + εi,t (10)

where zRigidityi,t is the rigidity level of contract i at date of contract signature t,Publici,t is the dummy variable indicating whether contract i signed at date t is apublic contract, Y is a vector of control variables, and εi,t is the error term (we assumethat εi,t (0,Σ)).

Then, we reduce the analysis scope on the subsample of public contracts in orderto explore the impact of political contestability on the contractual rigidity. Hence weestimate the following model:

zRigidityi,m,t = Xi,m,tα+ Yi,m,tβ + εi,m,t (11)

where zRigidityi,m,t is the rigidity level of contract i signed by the municipality m atdate t, X is a vector of variables measuring political contestability, Y is the same vectorof control variables than in equation (10) and εi,m,t is the error term (εit (0,Σ)).

4 Results

4.1 Public vs. Private Contract Rigidity

We first estimate contract rigidity of public vs. private contracts. Results are givenin Table 3. For six of the eight dimensions of contractual rigidity we identified, we see

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that public contracts are more rigid than private contracts. Overall, considering ourzRigidity measure, a public contract is more rigid than a private contract, especiallyconcerning zTermination, zArbitrage, zPenalties, zEvaluation, zLitigation, as well asdefining contingencies in contracts (zContingencies). Control variables also provideinteresting results. Indeed, results highlight the fact that renewed contracts are lessrigid than original contracts in two dimensions: termination and contingencies. Asexpected, provision of services contracts are much less rigid than operating ones. Onthe contrary, we do not find significant differences between operating and concessioncontracts. Finally, our variable Trend also seems to indicate that contracts tend tobe more rigid over time for five of the eight dimensions. These results corroborate ourProposition 1. We go a step further and turn to investigate how political contestabilityaffect the rigidity of public contracts.

4.2 Public Contract Rigidity and Political Contestability

Table 4 provides the results of estimations ran in our public contracts sub-sample inorder to explore the impact of the set of alternative political contestability measuresdefined in section 3.3.3. Three out of five of our model specifications using politicalcontestability variables suggest that political contestability might affect public contractrigidity. According to our Proposition 2, the more concentrated the political power in themunicipality, the less rigid the contract signed by the winning party after as illustratedby the positive and significant impact of our variableHHI in Model 1. Nevertheless, theHerfindahl-Hirschman Index is limited, notably because if fails to take into account thenumber and the concentration of non-winning lists. For that reason, we test alternativemeasure of political contestability. In model 2, we take into account the total number oflists that are running for the election and the concentration of all non-winning lists. Thesignificance of variables Number_Of_Lists and Residual_HHI indicates that contractsare more rigid when the political opposition is stronger.8

Similarly, we find a significant relationship between the rigidity of public contractsand the more or less comfortable margin of victory (Model 3). Indeed, our variableWin_Margin and Win_Margin2 suggest that contracts are more flexible when the po-litical contestability is weak and become more rigid when the political contestability ishigh. Models 1 to 3 leads to results consistent with our Proposition 2, however twoother of our specifications do not bring results concerning the political contestabilityeffect we are investigating: neither the distance from the contract date of signature tothe next election (Model 4) nor the observed swings at previous elections (Model 5)affect the level of contract rigidity.

There are many indicators of political contestability; however, the choice of an indi-8Theoretically, the number of lists have an ambiguous effect on contract rigidity. On the one hand,

the higher the number of lists, the higher the scrutiny over public decisions; on the other hand, thehigher the number of lists, the more fractioned the political benefits from a successful contract protest.Our results suggest that the first effect is prevalent.

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cator over another is not an easy task. Our results suggest that some of these dimensionsplay a role in public car park contracts’ rigidity in France. So far we provided corre-lations between the nature of contracts and their rigidity levels, as well as betweenpolitical contestability measures and public contract rigidity. If we control for manysources of heterogeneity between our contracts, notably by using geographical areasand year dummies, the reader might wonder if unobserved heterogeneity may be driv-ing the obtained results. More especially, contract duration, that differ between publicand private contracts may drive the results. In the next section we show first thatcontrolling for contract duration does not affect our main results. In addition, we inves-tigate renegotiation in contracts and find that, as expected, public contracts are moreoften renegotiated that private ones.

5 Robustness Checks

5.1 Contract Duration

Despite reduced to the scope of one sector, looking in details at our data we see thatpublic contracts are, on average, older and of longer term than private contracts (SeeFigure 3). Indeed, if investments differ between public and private contracts, leading tolonger term public contracts, this can explain the more frequent use of words trying todefine the transaction and the way to govern it, leading to more rigid contracts in ourdefinition. Consequently, their public feature would not be the issue. In order to takecare of this, we replicate our regressions including contract duration in our estimates.Table 5 provide results concerning rigidity of public vs. private contracts. Our mainresults are not affected. If contract duration appears to be correlated to some of ourrigidity dimensions, the main impact is still driven by the public vs. private nature ofcontracts.

As an additional robustness check, we also exclude concession contracts from ourdata: since we count only two private concession contracts (2% of the concession con-tracts sample), our results could be driven by the over-representation of public con-cession contracts. Thus, only focusing on operating and provision of services contractsallows for a fairer comparison among different level of contractual rigidity. Resultsprovided in Table 6 are highly similar. For five of the eight dimensions of contractualrigidity we identified, we see that public contracts are more rigid than private ones. Theonly change concerned the explained variable zContingencies, which is not surprisingbecause concession contracts are the longest ones and entail more details about futurecontingencies. Finally, we also run our estimates looking for the effect of political con-testability measures on the level of public contracts rigidity (see Table 7). Here again,our main results remain unaffected.

14

5.2 Rigidity and Renegotiations

Our set of results makes us confident about the specific nature of public contracts, lead-ing them to a higher level of rigidity compared to private contracts. Due to third-partyopportunism that pushes for rigid contracts at their initial stage, the same politicalhazards should also make public contracts be more formally renegotiated: since rela-tional contracting is not an option in such public contracts, each renegotiation shouldbe traduced into a formal amendment. In order to put this intuition to the test, weestimate the following model:

AverageAmendmentsi,t = zRigidityi,tγ + Publici,tα+ Yi,tβ + εi,t (12)

where AverageAmendmentsi,t is the number of amendments divided by the duration ofthe contract i, zRigidityit is the rigidity level of contract i at date of contract signaturet, Publici,t is the dummy variable indicating if contract i signed at date t is a publiccontract, Y is a vector of control variables and εi,t is the error term (we assume thatεi,t (0,Σ)). We use Two-Stage Least Squares estimations by instrumenting thevariable zRigidityi,t following our previous estimates in Model 1, 2, and 3 of Table4. Results are provided in Table 8.

As expected, public contracts are more often formally renegotiated in amendmentscompared to private contracts. A possible explanation is that public renegotiationsneed to be translated in formal amendments contrary to private contracts that mayrely on informal procedures. Also more rigid contracts appear to be less frequentlyrenegotiated, playing well their initial role.

6 Conclusions

In this paper we investigated the specific nature of public vs. private contracts. Wecompared procurement contracts where the procurer is either a public agent or a privatecorporation, and used algorithmic data reading and textual analysis on a dataset of carpark contracts the level of contratual rigidity. We found that public contracts featuremore rigidity clauses and that this rigidity is rising in political contestability by severalmeasures. We argue that a significant part of contractual rigidity difference betweenpurely private and public contracts is a political risk adaptation of the public agent tocurtail plausible challenges from political contesters and interest groups.

A natural consequence of public contract specificity is that they should be charac-terized by more frequent renegotiations and formal amendments. We found empiricalevidences that public contracts are more frequently renegotiated than private contractsand a negative correlation between rigidity levels and renegotiation rates, suggestingthat contracting parties that look for rigid contracts in order to avoid future renegotia-tions partly succeeded.

To our knowledge, this paper is the first to investigate the intrinsic properties of pub-

15

lic contracts compared to private contracts using data with measures of contract rigidity,frequency of amendments, and political contestatbility. It opens novel research avenuesto be explored. One of these promising avenue is to investigate how the frequency ofamendments in public contracts impact the quality of the contractual relationship andthe willingness of the parties to continue and renew their relationship. What can beinterpreted, at first glance, as a sign of weakness (i.e., frequent amendments) might wellbe, on the contrary, good news indicating that contracting parties are able to make thecontract adaptable through time.

16

Figu

re2:

Words

Freque

ncy—

Public

vs.Pr

ivateCon

tracts

17

Table2:

Descriptiv

eStatist

ics

All

sam

ple

Op

erat

ing

Con

trac

ts

Nm

σm

inm

axN

mσ

min

max

Public

436

0.89

0.32

01

173

0.83

0.38

01

zRigidity

436

2.30

17.7

1-2

8.01

88.2

517

37.

5020

.00

-24.

1188

.25

zDesign

436

0.06

1.52

-0.4

914

.09

173

0.37

2.06

-0.4

914

.09

zTermination

436

0.17

3.69

-2.3

924

.21

173

1.07

4.25

-2.3

914

.87

zArbitration

436

0.46

3.61

-4.6

221

.90

173

0.94

4.18

-4.6

221

.90

zPenalties

436

0.39

3.64

-4.6

922

.02

173

1.37

3.79

-4.6

922

.02

zCertification

436

0.22

3.16

-2.9

617

.74

173

0.65

3.43

-2.9

617

.21

zEvaluation

436

0.59

4.42

-5.4

826

.18

173

1.62

4.95

-5.3

026

.18

zLitigation

436

0.35

3.66

-4.5

920

.16

173

0.92

3.50

-4.5

912

.98

zCon

tingencies

436

0.01

2.71

-2.3

916

.70

173

0.21

3.30

-2.3

916

.70

Renew

ed43

60.

150.

360

117

30.

110.

310

1Inha

bitants

436

10.8

61.

588.

0914

.08

173

10.7

81.

398.

2514

.08

AverageAmendm

ents

436

0.19

0.33

02

173

0.18

0.28

01.

71Le

ft_Wing

436

0.14

0.34

01

173

0.15

0.36

01

Right_Wing

436

0.29

0.45

01

173

0.34

0.47

01

Trend

436

2000

.64

7.28

1985

2009

173

1999

.90

7.24

1985

2009

HHI

331

3934

.99

1170

.32

2143

.29

1000

012

938

87.7

310

75.8

621

43.2

967

05.8

2Residua

l_HHI

331

0.46

0.09

00.

6712

90.

470.

080.

340.

66Num

ber_

Of_

Lists

331

4.21

1.57

19

129

4.27

1.54

28

Win_Margin

331

21.7

316

.56

0.15

100

129

21.4

514

.99

0.31

63.4

4Win_Margin

233

174

5.47

1182

.03

0.02

1000

012

968

2.86

816.

310.

1040

24.4

9Distance

331

2.59

1.75

06

129

2.74

1.75

06

Swing_

Lag1

279

0.81

0.40

01

112

0.75

0.43

01

Pro

visi

onof

Serv

ices

Con

trac

tsC

once

ssio

nC

ontr

acts

Nm

σm

inm

axN

mσ

min

max

Public

166

0.89

0.31

01

970.

980.

140

1zR

igidity

166

-4.3

015

.08

-28.

0146

.94

974.

3413

.62

-27.

8443

.83

zDesign

166

-0.1

80.

89-0

.49

5.48

97-0

.07

1.14

-0.4

94.

96zT

ermination

166

-0.7

52.

75-2

.39

13.6

297

0.15

3.66

-2.3

924

.21

zArbitration

166

-0.0

63.

45-4

.62

17.2

597

0.51

2.57

-4.3

811

.03

zPenalties

166

-1.5

82.

63-4

.69

6.85

972.

033.

38-4

.69

8.27

zCertification

166

-0.3

93.

24-2

.96

17.7

497

0.49

2.22

-2.9

66.

58zE

valuation

166

-0.0

54.

13-5

.48

23.9

297

-0.1

53.

49-5

.48

12.4

5zL

itigation

166

-0.5

83.

87-4

.59

20.1

697

0.92

3.23

-4.5

916

.97

zCon

tingencies

166

-0.6

21.

96-2

.39

11.0

997

0.75

2.41

-2.3

910

.93

Renew

ed16

60.

270.

450

197

0.03

0.17

01

Inha

bitants

166

10.2

61.

278.

0914

.00

9712

.05

1.73

9.12

14.0

8AverageAmendm

ents

166

0.25

0.43

02

970.

120.

20

1.4

Left_Wing

166

0.04

0.19

01

970.

290.

460

1Right_Wing

166

0.36

0.48

01

970.

080.

280

1Trend

166

2005

.37

3.09

1986

2009

9719

93.9

06.

6419

8520

09HHI

146

3948

.10

1356

.38

2167

.06

1000

056

4009

.66

813.

9121

59.7

562

40.2

6Residua

l_HHI

146

0.45

0.11

00.

666

560.

490.

070.

350.

62Num

ber_

Of_

Lists

146

4.21

1.72

19

564.

091.

232

8Win_Margin

146

22.8

519

.14

0.15

100

5619

.45

12.1

30.

3149

.80

Win_Margin

214

688

6.16

1559

.13

0.02

1000

056

522.

8855

8.11

0.10

2480

.51

Distance

146

2.45

1.88

06

562.

571.

360

5Sw

ing_

Lag1

128

0.96

0.19

01

390.

460.

510

1

18

Table3:

Con

tractRigidity

—To

tala

ndCategories

Exp

lain

edva

riab

les:

zRigidity

zDesign

zTermination

zArbitrage

zPen

alties

zCertification

zEvaluation

zLitigation

zCon

ting

encies

Pub

lic12.141***

-0.516

1.443**

2.200**

3.281***

0.253

2.142*

2.165***

0.898*

(4.422)

(0.534)

(0.606)

(0.899)

(0.573)

(0.876)

(1.264)

(0.628)

(0.540)

Ren

ewed

-4.279+

-0.432

-0.934*

-0.499

-0.135

0.39

3-0.720

-0.808

-0.897**

(2.930)

(0.308)

(0.493)

(0.593)

(0.472)

(0.566)

(0.780)

(0.586)

(0.408)

Pro

visi

on_

of_

Serv

ices

-15.058***

-0.731***

-2.094***

-2.182***

-2.907***

-1.667***

-2.340***

-1.417***

-1.097**

(2.424)

(0.232)

(0.461)

(0.566)

(0.456)

(0.537)

(0.642)

(0.431)

(0.436)

Con

cess

ion

-1.259

0.096

-0.366

0.005

-0.128

0.517

-0.768

-0.382

-0.047

(2.666)

(0.230)

(0.510)

(0.515)

(0.610)

(0.460)

(0.649)

(0.551)

(0.445)

Inha

bita

nts

0.916

-0.071

0.214

0.186

0.075

0.075

0.466

0.124

-0.229

(1.300)

(0.111)

(0.273)

(0.279)

(0.226)

(0.248)

(0.351)

(0.292)

(0.161)

Left_

Win

g-0.150

0.009

-1.430*

-0.348

0.639

0.148

0.104

-0.004

0.471

(3.092)

(0.279)

(0.763)

(0.768)

(0.744)

(0.657)

(0.788)

(0.725)

(0.611)

Rig

ht_

Win

g3.913

0.269

1.161**

0.099

1.042**

1.165**

-0.259

0.917+

-0.559

(2.972)

(0.258)

(0.569)

(0.643)

(0.527)

(0.571)

(0.742)

(0.592)

(0.412)

Tren

d1.109**

0.033

0.164***

0.268***

0.044

0.174***

0.216*

0.078

0.101**

(0.435)

(0.055)

(0.063)

(0.066)

(0.071)

(0.067)

(0.120)

(0.081)

(0.048)

YearDum

mies

yes

yes

yes

yes

yes

yes

yes

yes

yes

Departm

entDum

mies

yes

yes

yes

yes

yes

yes

yes

yes

yes

Con

stan

t-2,245.568**

-64.393

-332.138***

-540.449***

-91.234

-350.664***

-439.943*

-161.032

-201.664**

(867.670)

(108.780)

(125.658)

(131.246)

(143.002)

(132.725)

(238.464)

(162.955)

(95.079)

N436

436

436

436

436

436

436

436

436

r20.340

0.246

0.275

0.298

0.437

0.241

0.303

0.354

0.244

Levelo

fsignifican

ce:***p<

0.01,*

*p<

0.05,*

p<0.1,

+p<

0.15

19

Table 4: Contract Rigidity and Political Contestability—Public Contracts SampleModel 1 Model 2 Model 3 Model 4 Model 5

Explained variable: zRigidityRenewed -3.908+ -3.565 -3.412 -3.010 -3.469

(2.629) (2.798) (2.868) (2.824) (2.921)Provision_of_Services -17.455*** -17.606*** -17.666*** -18.159*** -19.247***

(2.182) (2.563) (2.685) (2.624) (2.819)Concession -0.540 -2.732 -3.524 -3.338 -6.308+

(2.874) (3.501) (3.493) (3.518) (4.197)Inhabitants 0.660 -0.768 1.316 1.622 2.171

(1.197) (1.834) (1.618) (1.565) (2.026)Left_Wing 1.227 2.634 5.578 4.310 5.591

(3.854) (4.264) (4.432) (4.224) (4.827)Right_Wing 2.136 1.233 0.086 1.243 1.361

(2.373) (3.627) (3.810) (3.682) (3.847)Trend 0.682* 0.346 0.463 0.651 -0.129

(0.349) (0.490) (0.495) (0.923) (0.727)Political Contestability VariablesHHI -0.001* . . . .

(0.001) . . . .Residual_HHI . 24.811* . . .

. (12.836) . . .Number_Of_Lists . 2.672*** . . .

. (0.889) . . .Win_Margin . . 0.284* . .

. . (0.156) . .Win_Margin2 . . -0.005** . .

. . (0.002) . .Distance=1 . . . 7.255 .

. . . (14.346) .Distance=2 . . . 4.376 .

. . . (12.403) .Distance=3 . . . 3.237 .

. . . (10.315) .Distance=4 . . . -5.022 .

. . . (15.383) .Distance=5 . . . 7.125 .

. . . (10.933) .Distance=6 . . . 7.905 .

. . . (17.003) .Swing_Lag1 . . . . 1.992

. . . . (4.642)Year Dummies yes yes yes yes yesDepartment Dummies yes yes yes yes yesConstant -1,356.617* -712.762 -949.237 -1,324.979 238.045

(700.262) (984.268) (994.036) (1,834.238) (1,458.670)N 331 331 331 331 279r2 0.251 0.427 0.424 0.411 0.448Level of significance: *** p<0.01, ** p<0.05, * p<0.1, + p<0.15

20

Figure 3: Contract Duration—Public vs. Private Contracts

21

Table5:

Con

tractRigidity

—To

tala

ndCategories(w

ithcontract

duratio

n)E

xpla

ined

vari

able

s:zR

igidity

zDesign

zTermination

zArbitrage

zPen

alties

zCertification

zEvaluation

zLitigation

zCon

ting

encies

Pub

lic11.530**

-0.541

1.231**

2.204**

3.070***

0.08

12.141*

2.089***

0.957*

(4.463)

(0.537)

(0.616)

(0.893)

(0.575)

(0.881)

(1.274)

(0.637)

(0.502)

Ren

ewed

-4.329+

-0.434

-0.951*

-0.499

-0.153

0.379

-0.720

-0.815

-0.892**

(2.928)

(0.309)

(0.488)

(0.594)

(0.461)

(0.565)

(0.781)

(0.589)

(0.406)

Dur

atio

n0.133

0.005

0.046*

-0.001

0.046*

0.037**

0.000

0.017

-0.013

(0.097)

(0.009)

(0.026)

(0.022)

(0.026)

(0.018)

(0.025)

(0.025)

(0.024)

Pro

visi

on_

of_

Serv

ices

-14.393***

-0.703***

-1.862***

-2.186***

-2.677***

-1.479***

-2.338***

-1.334***

-1.160**

(2.392)

(0.234)

(0.444)

(0.575)

(0.444)

(0.533)

(0.653)

(0.436)

(0.459)

Con

cess

ion

-2.399

0.049

-0.762

0.011

-0.521

0.196

-0.771

-0.524

0.061

(2.683)

(0.236)

(0.587)

(0.501)

(0.636)

(0.491)

(0.664)

(0.601)

(0.460)

Inha

bita

nts

0.886

-0.073

0.203

0.186

0.065

0.067

0.466

0.120

-0.226

(1.286)

(0.112)

(0.274)

(0.279)

(0.219)

(0.247)

(0.351)

(0.291)

(0.163)

Left_

Win

g-0.548

-0.007

-1.569**

-0.346

0.501

0.03

50.104

-0.054

0.509

(3.098)

(0.277)

(0.768)

(0.754)

(0.750)

(0.643)

(0.782)

(0.707)

(0.620)

Rig

ht_

Win

g3.666

0.259

1.075*

0.100

0.957*

1.09

5*-0.260

0.886+

-0.535

(2.976)

(0.260)

(0.561)

(0.652)

(0.517)

(0.573)

(0.749)

(0.596)

(0.427)

Tren

d1.223***

0.038

0.204***

0.267***

0.083

0.20

6***

0.216*

0.092

0.090*

(0.465)

(0.056)

(0.070)

(0.071)

(0.080)

(0.070)

(0.124)

(0.089)

(0.051)

YearDum

mies

yes

yes

yes

yes

yes

yes

yes

yes

yes

Departm

entDum

mies

yes

yes

yes

yes

yes

yes

yes

yes

yes

Con

stan

t-2,474.266***

-73.871

-411.630***

-539.286***

-170.038

-415.005***

-440.378*

-189.525

-179.825*

(927.061)

(110.648)

(139.551)

(141.130)

(161.514)

(140

.051)

(247.620)

(177.207)

(102.924)

N436

436

436

436

436

436

436

436

436

r20.343

0.247

0.283

0.298

0.445

0.248

0.303

0.355

0.245

Levelo

fsignifican

ce:***p<

0.01,*

*p<

0.05,*

p<0.1,

+p<

0.15

22

Table6:

Con

tractRigidity

—To

tala

ndCategories(w

ithcontract

duratio

nan

dwith

outconc

essio

ncontracts)

Exp

lain

edva

riab

les:

zRigidity

zDesign

zTermination

zArbitrage

zPen

alties

zCertification

zEvaluation

zLitigation

zCon

ting

encies

Pub

lic11.660**

-0.447

1.073+

2.296**

3.227***

-0.112

2.634*

1.843**

0.802+

(5.251)

(0.612)

(0.688)

(1.054)

(0.627)

(1.020)

(1.491)

(0.740)

(0.494)

Ren

ewed

-4.027

-0.398

-0.756

-0.696

-0.108

0.235

-0.860

-0.725

-0.615+

(3.260)

(0.358)

(0.537)

(0.653)

(0.478)

(0.642)

(0.879)

(0.642)

(0.424)

Dur

atio

n0.238*

-0.012

0.094**

0.000

0.096***

0.027

0.003

0.029

0.002

(0.129)

(0.012)

(0.037)

(0.030)

(0.035)

(0.019)

(0.029)

(0.033)

(0.030)

Pro

visi

on_

of_

Serv

ices

-14.631***

-0.847***

-1.619***

-2.312***

-2.414***

-1.353**

-2.937***

-1.394***

-1.108**

(2.599)

(0.263)

(0.493)

(0.642)

(0.469)

(0.626)

(0.708)

(0.472)

(0.510)

Inha

bita

nts

1.710

-0.081

0.272

0.320

0.283

0.033

0.723*

0.212

-0.130

(1.448)

(0.137)

(0.282)

(0.315)

(0.224)

(0.283)

(0.386)

(0.316)

(0.165)

Left_

Win

g0.346

0.814**

-0.582

-0.557

0.495

0.268

-0.641

0.053

0.715

(4.601)

(0.394)

(0.914)

(1.345)

(1.091)

(0.792)

(0.964)

(1.151)

(1.092)

Rig

ht_

Win

g3.698

-0.051

0.695

0.385

0.709

1.22

9*-0.383

1.213*

-0.199

(3.273)

(0.282)

(0.579)

(0.726)

(0.533)

(0.639)

(0.813)

(0.671)

(0.452)

Tren

d1.798***

0.142**

0.350***

0.347***

0.075

0.172*

0.387***

0.155

0.095**

(0.537)

(0.062)

(0.095)

(0.101)

(0.056)

(0.098)

(0.143)

(0.116)

(0.047)

YearDum

mies

yes

yes

yes

yes

yes

yes

yes

yes

yes

Departm

entDum

mies

yes

yes

yes

yes

yes

yes

yes

yes

yes

Con

stan

t-3,638.768***

-283.344**

-706.397***

-701.394***

-156.442

-346.749*

-785.226***

-316.619

-191.603**

(1,068.834)

(123.844)

(190.627)

(202.593)

(113.350)

(195

.385)

(284.060)

(232.377)

(94.255)

N339

339

339

339

339

339

339

339

339

r20.393

0.292

0.381

0.326

0.547

0.284

0.365

0.368

0.278

Levelo

fsignifican

ce:***p<

0.01,*

*p<

0.05,*

p<0.1,

+p<

0.15

23

Table 7: Contract Rigidity and Political Contestability—Public Contracts Sample (withcontract duration)

Model 1 Model 2 Model 3 Model 4 Model 5Explained variable: zRigidityRenewed -3.174 -3.542 -3.393 -2.984 -3.434

(2.814) (2.791) (2.862) (2.823) (2.923)Duration 0.148 0.150 0.157 0.137 0.092

(0.117) (0.117) (0.118) (0.120) (0.147)Provision_of_Services -17.147*** -16.606*** -16.591*** -17.244*** -18.657***

(2.640) (2.634) (2.726) (2.653) (2.864)Concession -4.436 -3.990 -4.867 -4.501 -7.217+

(3.566) (3.525) (3.534) (3.588) (4.380)Inhabitants 0.240 -0.763 1.426 1.711 2.205

(1.577) (1.797) (1.604) (1.551) (2.031)Left_Wing 4.208 2.114 5.151 3.822 5.141

(4.165) (4.291) (4.485) (4.292) (4.864)Right_Wing 1.052 0.798 -0.456 0.825 1.026

(3.605) (3.623) (3.824) (3.695) (3.959)Trend 0.480 0.412 0.537 0.555 -0.051

(0.522) (0.502) (0.508) (0.952) (0.752)Political Contestability VariablesHHI -0.002** . . . .

(0.001) . . . .Residual_HHI . 24.520* . . .

. (12.734) . . .Number_Of_Lists . 2.736*** . . .

. (0.890) . . .Win_Margin . . 0.304** . .

. . (0.153) . .Win_Margin2 . . -0.005*** . .

. . (0.002) . .Distance=1 . . . 8.536 .

. . . (14.532) .Distance=2 . . . 4.502 .

. . . (12.406) .Distance=3 . . . 3.253 .

. . . (10.253) .Distance=4 . . . -2.169 .

. . . (11.714) .Distance=5 . . . 10.340 .

. . . (17.444) .Distance=6 . . . 10.875 .

. . . (17.537) .Swing_Lag1 . . . . 1.895

. . . . (4.596)Year Dummies yes yes yes yes yesDepartment Dummies yes yes yes yes yesConstant -958.462 -846.978 -1,099.694 -1,138.043 80.626

(1,048.347) (1,008.750) (1,020.284) (1,891.539) (1,510.336)N 331 331 331 331 279r2 0.426 0.431 0.428 0.414 0.450Level of significance: *** p<0.01, ** p<0.05, * p<0.1, + p<0.15

24

Table 8: Average Renegotiations—Two-Stage Least Square (zRigidity instrumented)Model 1a Model 1b Model 2a Model 2b Model 3a Model 3b

Explained variable: AverageAmendmentszRigidity -0.006*** -0.006*** -0.006*** -0.006*** -0.006*** -0.006***

(0.002) (0.002) (0.002) (0.002) (0.002) (0.002)Public 0.094* 0.153*** 0.121** 0.167*** 0.123** 0.168***

(0.050) (0.054) (0.057) (0.059) (0.057) (0.059)Renewed -0.185*** -0.231*** -0.179*** -0.223*** -0.180*** -0.223***

(0.038) (0.041) (0.039) (0.042) (0.039) (0.043)Inhabitants -0.024*** -0.010 0.024 0.040** 0.024 0.040**

(0.009) (0.010) (0.017) (0.017) (0.017) (0.017)Duration . -0.005*** . -0.005*** . -0.005***

. (0.001) . (0.001) . (0.001)Year Dummies yes yes yes yes yes yesConstant 0.413*** 0.289** -0.096 -0.231 -0.098 -0.234

(0.119) (0.120) (0.188) (0.192) (0.189) (0.193)N 436 436 436 436 436 436r2 0.24 0.27 0.26 0.29 0.25 0.29Instruments for Rigidity

HHI HHI Residual_HHI Residual_HHI Win_Margin Win_MarginNumber_Of_Lists Number_Of_Lists Win_Margin2 Win_Margin2

Level of significance: *** p<0.01, ** p<0.05, * p<0.1, + p<0.15

25

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