The effect of bidding success inconstruction bidding

Bee Lan OoSchool of Civil Engineering, The University of Sydney, Sydney, Australia

Hing-Po LoDepartment of Management Sciences, Hong Kong City University,

Hong Kong, China, and

Benson Teck-Heng LimFaculty of Built Environment, The University of New South Wales,

Sydney, Australia

Abstract

Purpose – Winning a bid will carry implications for capacity level of a construction firm. This paperaims to examine the impact of a winning bid on contractors’ bid pricing strategies.

Design/methodology/approach – In identifying the specific types of bidding trends before andafter a winning bid, the variations in bids are expressed as a function of time relative to winning bid –the “event” of interest in this study – using a piecewise mixed effects model. The bids analysedcomprised series of bids with a winning bid in between, recorded from Hong Kong buildingcontractors.

Findings – The results show that there is a relationship between bid price and bidding success. Thebidders in general bid low for time periods before a winning bid and they are less competitive in timeperiods after a winning bid. However, by considering the individual bidders’ characteristics that relateto differences in bidding competitiveness, it is shown that there is remarkable heterogeneity among thebidders in bid pricing decision for pre- and post-winning periods. Nevertheless, the statisticallysignificant bidding trends before and after a winning bid strengthen the notion that systematicchanges in bidding behaviour over time do occur in reality in response to changes in firm capacitylevel.

Originality/value – This empirical investigation provides strong evidence on the systematicchanges in bidding behaviour over time in response to changes in firm capacity level, supporting theneed to incorporate firm capacity level in the future development of a suitable theoretical frameworkon construction bidding.

Keywords Firm capacity, Winning bid, Bidding trend, Construction industry, Companies, Tendering

Paper type Research paper

IntroductionThere has been no apparent progress in the theoretical framework of buildingeconomics (Runeson, 1997). In particular, he pointed out that the theoreticaldevelopment of tendering (bidding) theory, which is conventionally referred to as partof building economics, has been slow. Of the few studies to date aimed at analysing theapplicability of different theories on construction bidding, Runeson and Raftery (1998)argue that neoclassical microeconomic theory is prefer to Gate’s (1967) bidding theory,which Skitmore et al. (2006) have supported in contrast to full-cost pricing theory.Skitmore and Smyth (2007) have further examined construction bid pricing frommarketing viewpoints and the challenges from marketing perspective in applying

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Engineering, Construction andArchitectural Management

Vol. 19 No. 1, 2012pp. 25-39

q Emerald Group Publishing Limited0969-9988

DOI 10.1108/09699981211192553

neoclassical microeconomic theory in practice. These previous studies have identifiedthe conceptual and practical limitations in the theories examined and advocate that, inorder to progress, further exploration of pricing practices via empirical work isrequired to establish empirical regularities as a basis for a suitable theoreticalframework on construction bidding. This leaves little room for doubt that real-worldbid pricing practices in the construction industry are complex. The pricing practicesare further compounded by the special characteristics of the industry, which includethe high level of uncertainty in demand level, separation of design and productionprocesses, and the lumpiness of construction demand and supply (Skitmore et al.,2006). Indeed, demand uncertainty is sufficient to produce heterogeneity amongcompetitors (Lippman et al., 1991), especially since there can be significant problemsassociated with demand forecasting in construction (Males, 1991). The condition ofheterogeneity puts contractors at varying predispositions for bidding decisions, withvarying degrees of preference or sensitivity placed on factors affecting their biddingdecisions (Oo et al., 2007a, 2008, 2010a).

In construction bidding, contractors’ decision making on pricing has been found tobe subject to exogenous and endogenous variables, which vary in response to thecontext within which they are considered (e.g. Ahmad and Minkarah, 1988; Shash,1993). With pricing objective(s) differing from contractor to contractor, approaches tobid pricing are therefore unique to individual construction firms. Essentially, they needto win jobs by targeting at bid opportunities that assist in meeting firms’ objectives.Empirical research detected that contractors are selective in their bid/no-bid decisions(e.g. Odusote and Fellows, 1992; Lowe and Parvar, 2004; Oo et al., 2008), recognisingthere are resource implications in recurrent competitive bidding. Winning a particularjob will carry implications for capacity level of a firm, i.e. the resources available toundertake future contracts. Previous studies also indicates that there is littlerandomness in bidding as contractors’ bids vary with capacity utilisation and generalmarket conditions (e.g. Flanagan and Norman, 1985; Runeson and Skitmore, 1999).

This paper examines the impact of a winning bid on contractors’ bid pricingstrategies. The relationship between bid price (mark-up) and bidding success isexplored using a piecewise mixed effects model. Instead of using contract sequencenumber or date order that determines the frequency of a contractor’s bidding attempts,the variations in bid are expressed as a function of time relative to winning bid – the“event” of interest in this study. In this way, the specific types of bidding trends beforeand after a winning bid are considered. The identified bidding trends provide strongevidence on the impact of a winning bid on contractors’ bid pricing strategies. Inparticular, this empirical investigation adds to both our theoretical and empiricalunderstanding of the systematic changes in bidding behaviour over time in response tochanges in firm capacity level, supporting the need to incorporate firm capacity level inthe future development of a suitable theoretical framework on construction bidding.

Winning a bidContractors adopt various bidding strategies to enhance their chances of winningwork. In a survey of Canadian contractors, Fayek et al. (1999) found that the mostimportant objective in bid pricing is to win jobs. It follows, therefore, that contractorswould submit low bids (i.e. competitive bids with low mark-ups) to increase successrate. In practice, however, empirical evidence indicates that contractors do submit high

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bids or cover prices in some instances. They would still bid even when they do notexpect to win for varying reasons. These include:

. to show they are still in market;

. to keep abreast of the current market conditions since the only reliable means isto complete an estimate for a particular bid opportunity and compare that to thewinning bid (Runeson, 2000);

. to make it more difficult for their competitors to resolve their strategy (Drew,1994);

. to deny their competitors the chance of entering the competition in their place(Drew, 1994); and

. to stay in favour with clients in securing future bidding opportunities (Collinsand Pasquire, 1996).

Low bids, on the other hand, claim concern for the contractors’ pricing practice.Contractors’ mark-up in bid pricing may represent a “mark-down” in certain settings,i.e. submitting a bid with low or zero probability of profit. As remarked by Runeson(2000), it is often rational for contractors to do so, if the anticipated cost of not winningthe bid and carrying the expenses of unutilised capacity is greater than the anticipatedloss of executing the contract at the bid price. This phenomenon has been termed as“buying work” and seen as a pricing tactics in order to remain in business (Fellows andLangford, 1980). They further pointed out that buying work may due to contractors’desperation to survive in recession, although it is seen unattractive and decreaseshort-term profitability, it may lead to potential project in future and keep thecompany’s resources “moving”. Oo et al. (2010a) detected that contractors prefer smallcontracts that can be completed within short periods of time in recession, with theprimary goal to survive the recession and wait for next boom in the constructionmarket. Dyer and Kagel (1996) refer this phenomenon as simple survivorship pressurethat applied to both new market entrants as well as experienced contractors. It appears,therefore, that pricing in construction is market oriented (Skitmore et al., 2006).Contractors’ mark-up decision in bid pricing is sensitive to the market conditions, ormore precisely, the changes in demand and capacity utilisation (Runeson, 2000).

Empirical studies have shown quite conclusive that bid prices do change inresponse to changes in the level of demand (e.g. Carr and Sandahl, 1978: Runeson, 1988:Chan et al., 1996). A classical demonstration of this is in de Neufville et al. (1977) wheremark-ups are systematically varied between “good” and “bad” years, i.e. years with thegreatest and least activity for contractors, respectively. They found that contractorsbid noticeably lower in bad than in good years. Such variations in bids have beenfound to be associated with contractors’ need for work. Using an experimental settingthat examined two market conditions scenarios, namely: “boom times with high needfor work”, and “recession times with low need for work”, Oo et al. (2007b) haveobtained very similar, highly significant results. The need for work is seen as areflection of the capacity utilisation of a firm. A contractor can be expected to submit arelatively high bid when its need for work is low (i.e. with little spare capacity) and arelatively low bid when its need for work is high (i.e. with extensive spare capacity),even on projects that are identical in all other respects (Flanagan and Norman, 1985).They demonstrated that this variability in pricing is because opportunity costs – the

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currently available resources, and the effect on resource availability of winning aparticular bidding competition – are likely to vary between contractors and over time.According to their analysis where a bid comprised both the direct costs andopportunity costs of a project, opportunity costs may approach zero if there isextensive spare capacity, thus lowering the bid.

In considering the periodicity involved in capacity utilisation, winning a bid tooearly when a contractor has no spare capacity necessitates a higher price, as thecontractor need to employ new factors of production in order to expand its optimumcapacity, and winning a bid too late means that the contractor has to pay a cost forcarrying unutilised capacity (Runeson and Skitmore, 1999). They claim that a rationalapproach would be to vary the mark-up as indicated in McCaffer and Pettitt’s (1976)cusum curve. That is, to start with a high mark-up and systematically reduce it tomake the bid more competitive as the need for new job becomes more urgent. InMcCaffer and Pettitt’s cusum curve, the cumulative sums (cusum) of [(bid – meanbid)/mean bid] some 600 contracts involving almost 400 contractors were plottedagainst the contract sequence number. They found that 85 per cent of winning bidswere preceded by increasingly more competitive bids, until the contractors win a bid.After the winning bids, less competitive bids were recorded, as the contractors werenot so eager to win a job. However, in a recent study by Skitmore and Runeson (2006)that aimed at testing the statistical significance of the bidding trends detected byMcCaffer and Pettitt (1976), they found that:

. winning bids are not in general preceded by increasingly more competitive bids;and

. the trend of high and low bids over a period of time is most likely due to thepresence of highly uncompetitive bids or outliers.

In their analysis comprised bids from eight bidders, they have not considered the lesscompetitive bidding trend after a winning bid detected in McCaffer and Pettitt’s cusumcurve. Although these two empirical studies have not applied modelling techniques toprovide statistics concerning significance of bidding trends before and after a winningbid, they are considered the closest studies that provide a direction for empiricalinvestigation in this study. Here, we use a piecewise mixed effects modelling approachto model the process of changes in the bid price of building work before and after awinning bid. It aims to further test the McCaffer and Pettitt’s cusum curve,hypothesising that “winning bids are preceded by increasingly more competitive bids,which will then be followed by less competitive bids”.

DatasetThe dataset needed for the analysis are difficult to obtain since the data collectionprocess is time consuming and expensive, if the clients do not publicly disclose theirbidding data. Although contractors could have access to their competitors’ bids from avariety of sources, including: competitors, subcontractors, friendly acquaintances,suppliers and newspapers (Drew and Fellows, 1996), it is likely that the completenessand accuracy of the dataset are questionable. Nevertheless, a complete set of bids for allbuilding contracts let by the Hong Kong Architectural Services Department from 1990to 1996 was obtained for the analysis. It comprised 266 building contracts published inFu et al. (2002). Of these building contracts, 203 are building works and 63 are

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alteration and extension works to existing buildings with average contract values ofHK$134 million and HK$97 million (at 1996 prices), respectively. There were85 medium- to large-size construction firms compete for the jobs with a total of 3,560bids recorded in the dataset.

A set of criteria were applied to extract longest series of bids recorded from eachbidder for modelling the effect of bidding success. For each series of bids, there must beat least one observation (bid) recorded before and after a winning bid (i.e. the event). Inthe case where there were consecutive winning bids in a bid series, which do notconstitute a single “event”, the respective series were not included in the analysis. Uponthe extraction, 1,778 bids from 67 bidders (i.e. 67 series of bids) were included in themodelling attempt. Table I provides the overall frequency of bids with an average of26.5 bids recorded per bidder. The majority (55 per cent) of the bidders have 11 to30 bids recorded in their longest series of bids with a winning bid in between. However,there are a few bidders (9 per cent) with very large number of bids, ranging from 51 to80 bids recorded in their longest series of bids.

For the frequency of pre- and post-winning bids, around 50 per cent of the biddershad submitted within a range of up to ten bids before and after a winning bid as shownin Table II. Also, there are a few bidders with 31 to 60 bids recorded for pre- andpost-winning periods, and the remaining bidders are with 11 to 30 pre- andpost-winning bids. It can also be seen that the average number of bids recorded per

Pre-wining Post-winningNo. of bids per bidder No. of bidders (%) No. of bidders (%)

1 to 10 36 53.7 33 49.311 to 20 18 26.9 24 35.821 to 30 7 10.4 6 9.031 to 40 3 4.5 2 3.041 to 50 1 1.5 0 0.051 to 60 2 3.0 2 3.0Total 67 67Total bids 902 809Mean bids per bidder 13.46 12.07

Table II.Overall frequency of pre-

and post-winning bids

No. of bids per bidder No. of bidders (%)

1 to 10 7 10.411 to 20 24 35.821 to 30 13 19.431 to 40 10 14.941 to 50 7 10.451 to 60 4 6.061 to 70 1 1.571 to 80 1 1.5Total 67 100.0Total bids 1,778Mean bids per bidder 26.53

Table I.Overall frequency of bids

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bidder for pre- and post-winning periods are very close, i.e. between 12 and 13 bids,suggesting a winning bid in the middle of an average series comprising 26.5 bids.

Exploratory analysisIn examining the impact of a winning bid on contractors’ bid pricing strategies, thedependent variable is competitiveness between bids by considering bids in relation to abaseline. In the analysis that follows, the lowest bid was taken to mean the “winningbid” that forms the baseline in measuring competitiveness in bidding. This is justifiedbecause the majority (87 per cent) of the contracts in the existing dataset were awardedto the lowest bidders (Fu et al., 2002). The contractors’ bidding performance for eachcontract is expressed as a bidding competitiveness ratio (BCR) as given below:

BCR ¼ xð1Þ=x ð1Þ

where x(1) is the lowest bid and x is the contractor’s bid. A value of unity indicatesmaximum competitiveness presented by the winning bid. A higher BCR indicatesgreater bidding competitiveness and vice versa, with maximum and minimumcompetitiveness being constrained between one and zero.

An exploratory analysis was conducted to check for the presence of unusualfeatures in the dataset and to visualise the research hypothesis. Figure 1 shows ascatter plot of the entire set of 1,778 bids in which the BCR was plotted against timerelative to winning bid. It can be seen that number of bids in pre- and post-winningperiods is largely within the range of 25 bids. Also, there are some relatively

Figure 1.Bidding competitivenessratio with Lowess curve

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uncompetitive bids with low BCR values. It appears that these uncompetitive bids arenot entirely random and it is possible that they are “cover prices”. Here, theuncompetitive bids have been included in subsequent analysis given that cover pricesdo regularly occur in bidding competitions for varying reasons identified in literature.

In revealing the general pattern in BCR trend with respect to the time of winningbid, a Lowess curve was fitted in Figure 1 using non-parametric robust local smoothingprocedure (Hardle, 1990). This allows for an informal check of non-linearity in the BCRtrend. It can be seen that the Lowess curve remains flat prior to winning bids and startsto rise sharply near the time of wining bids, and it follows a gently down slopeimmediately after winning bids and becomes flat thereafter. To examine the BCR trendfurther, Table III shows the summary statistics for the bidders’ pre- and post-averages.It is now clear that the BCR average in pre-winning period is higher than thecorresponding BCR in post-winning period. This suggests that bids in pre-winningperiod are more competitive than post-winning bids in general. Also, the resultantstandard deviation (SD) estimates suggest that the bidders’ consistency in biddingdoes not change remarkably over the pre- ðSD ¼ 0:1040Þ and post-winning ðSD ¼0:1049Þ periods. It therefore seems that the bidders had not submitted highlyuncompetitive bids immediately after a winning bid. This observation is likely to bebecause of the intense bidding competition in the Hong Kong construction markets (theaverage number of bidders in the existing dataset was 13). The contractors werewilling to bid competitively to increase their bidding success rate (the average biddingsuccess rate is around 4 per cent based on an average of 26.5 bids recorded per bidder),even though they appear to have submitted cover prices as detected in Figure 1.

Research hypothesisWe hypothesise that winning bids are preceded by increasingly more competitive bids(i.e. higher BCR), which will then be followed by less competitive bids (i.e. lower BCR).Graphical representation of the research hypothesis and the modelling approach areshown schematically in Figure 2. The results from exploratory analysis on samplemeans of pre- and post-winning periods at ten bids, were used to make the graph realisticand to reflect the time of measurements relative to winning bid. It assumes that eachbidder has a two-piece linear spline curve with a knot at the time of winning bid. In this,the piecewise mixed effects modelling approach assigns a pre-winning slope b1 and apost-winning slope b2 separated by the winning bid event as detailed next.

Piecewise mixed effects modelThe piecewise mixed effects modelling approach assumes that a continuous dependentvariable is linearly related to a set of independent variables, allows two separate slopesto be fitted simultaneously using all data points – representing the periods pre- andpost-event (see Naumova et al., 2001). Also, it allows one to account for correlation

Time period Min. Median Mean Max. Var. SD

All period 0.2795 0.8731 0.8547 1.0000 0.0113 0.1064Pre-winning 0.2795 0.8701 0.8503 0.9996 0.0108 0.1040Post-winning 0.3353 0.8675 0.8476 0.9988 0.0110 0.1049

Table III.Descriptive statistics

for BCR

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between observations collected over time, and it does not require the same number ofobservations on each respondent (subject) nor that the measurements be taken at thesame set of measurement occasions (Fitzmaurice et al., 2004). This flexibility inaccommodating any degree of imbalance in repeated measures data that make use of allmeasurements available is an important consideration in bidding models, recognisingthat contractors do not always bid for every job that comes along, and that each biddingopportunity is of different measurement occasions (e.g. different project type and size).The idea here is to express BCR as a function of time relative to winning bid, obtainingone intercept and two slopes: one for before and one for after the winning bid. Let tij be thetime of j-measurement for i-subject before (tij, 0) or after (tij$ 0) a winning bid; and dijbe an indicator: dij ¼ 1 for time period pre-winning and dij ¼ 0 for time periodpost-winning. Now, the piecewise mixed effects model can be written as follows:

BCRij ¼ ðb0 þ b0iÞ þ ðb1 þ b1iÞtijdij þ ðb2 þ b2iÞtijð1 2 dijÞ þ 1ij ð2Þ

where tijdij and tij(1- dij) are the time of j-measurement for i-subject corresponding topre-and post-winning time periods, and there are two sets of parameters in the model.Parameters b0, b1, b2 are the population mean effects (i.e. the fixed effects shared by allsubjects), whereas parameters b0i, b1i, b2i are subject-specific effects (i.e. the randomeffects that are unique to each subject). In this mixed effects model, fixed effects, b andrandom effects, b are connected to each other, so that any observable effect is acombination of the two. For example, (b1 þ b1i) is the i th subject’s slope, or rate ofchange in BCR before a winning bid. It demonstrates the extension of the model todetermine individual bidder characteristics (b0i, b1i, b2i) that relate to differences in BCR.Such parameters are of particularly valuable to the understanding of inherentheterogeneity among bidders in decision making for pricing before and after winningbids. It is noted that mixed effects modelling approach has been used for modelling theheterogeneity in contractors’ mark-up behaviour (Oo et al., 2010a), and for competitoranalysis in construction bidding (Oo et al., 2010b).

ResultsFollowing the mixed effects model building process in Verbeke and Molenberghs(2000), both the MIXED procedure in SPSS and the PROC MIXED procedure in SASwere used in this study to obtain the model parameter estimates and their standard

Figure 2.Graphical representationof the research hypothesisand the modellingapproach

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errors. Table IV contains the parameter estimates for the model fixed effects and thecorresponding 95 per cent confidence intervals. Table V, on the other hand, containsthe random effects estimation (or known as empirical “Best Linear Unbiased Predictor(BLUP)) for individual bidders” intercepts and two slopes.

We first examine the fixed effects estimates, the results indicate that the pre- andpost-winning slopes have the expected signs that support the research hypothesispostulated in Figure 2. In this, the population mean BCR is associated with an increaseof 0.0017 for each bid prior to a winning bid; and a decrease of 0.0019 for each bid aftera winning bid. Although the slopes are rather shallow, they are statistically significantat the conventional p, 0.05 cut-off level. Also, the fixed effects estimates indicate thatthere is only a small difference between the pre- and post-winning slopes. Thissuggests that both the upward and downward trends in the population mean BCR overa winning bid are of comparable magnitude. Further evidence of the small differencebetween the pre- and post- winning slopes can be found by examining the difference inpredicted population mean BCR using the fixed effects estimates only. A t-testdemonstrates that the difference is not statistically significant at p, 0.05 cut-off level.

In examining Table V, it can be seen that the empirical BLUPs are of both positiveand negative signs, indicating that the individual bidders’ responses to the predictorvariables are either above or below the population mean. For example, the intercept forBidder 1,001 of positive sign ðb01 ¼ 0:04865Þ indicates that the “true” BCR at winningbid of this bidder is above of the population mean based on the model parameter(b0 þ b0i) in Equation 2. The term “true” BCR is used to remind reader that this b0i is aparameter in the piecewise mixed model since the actual BCR when other parametersin the model are zero is not observed and not estimable.

To examine both the fixed and random effects estimates of the piecewise mixedeffects model, we can substitute the empirical BLUPs into Equation 2 in obtaining themean BCR profile of each bidder in the sample involved. Figure 3 displays theillustrative plot of the predicted population mean BCR profile (fixed effects only) andthe predicted individual mean BCR profiles for Bidders 1,001 and 1,031. The observedindividual mean BCR profile is imposed for illustrative purposes. It can be clearly seenthat the predicted individual mean BCR profile of Bidder 1,001 is discernibly above thepredicted population mean profile, mainly due to the positive empirical BLUPs for therandom intercept (i.e. 0.04865). This suggests that Bidder 1,001 had submitted morecompetitive bids with mean BCR greater than the population mean, despite a fewhighly uncompetitive bids observed before a winning bid. The individual mean BCRprofile of Bidder 1,031, however, follows a decreasing trend before and after a winningbid. This individual profile differs from the population mean BCR profile or thehypothesised BCR profile. It appears that Bidder 1,031 is less serious in its biddingattempts as reflected in recorded “wild” uncompetitive bids (BCR below 0.80),

Parameter Estimate Std. Error t Sig.95% confidence interval

Lower bound Upper bound

Intercept, b0 0.8684 0.0056 155.660 0.000 0.8573 0.8794Pre-winning slope, b1 0.0017 0.0006 2.753 0.015 0.0004 0.0029Post-winning slope, b2 20.0019 0.0006 23.275 0.005 20.0031 20.0007

Table IV.Parameter estimates for

the fixed effects

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Intercept, b0i Pre-winning slope, b1i Post-winning slope, b2i

Bidder Estimate Std. Error Estimate Std. Error Estimate Std. Error

1,001 0.04865 0.0177 * * 20.00151 0.0016 20.00104 0.00161,002 20.01510 0.0181 20.00115 0.0019 20.00043 0.00161,003 0.00603 0.0221 0.00020 0.0022 20.00003 0.00171,004 20.00889 0.0175 0.00132 0.0016 0.00028 0.00151,005 0.01863 0.0206 0.00010 0.0021 20.00013 0.00171,006 0.00145 0.0206 0.00134 0.0020 0.00018 0.00171,007 0.03942 0.0190 * * 0.00001 0.0022 20.00021 0.00161,008 20.00416 0.0187 0.00127 0.0016 20.00023 0.00171,009 0.00553 0.0173 20.00248 0.0019 20.00150 0.00101,010 20.00589 0.0251 20.00034 0.0022 20.00006 0.00171,011 0.02111 0.0244 20.00018 0.0022 20.00018 0.00171,012 20.05973 0.0208 * * 20.00241 0.0021 0.00001 0.00171,013 0.02574 0.0184 20.00054 0.0021 20.00009 0.00161,014 20.02765 0.0186 20.00039 0.0022 20.00102 0.00111,015 20.02681 0.0268 20.00002 0.0022 0.00009 0.00171,016 20.00340 0.0221 20.00069 0.0021 20.00004 0.00171,017 20.03968 0.0198 * * 20.00106 0.0020 0.00056 0.00171,018 0.01514 0.0197 0.00006 0.0022 20.00044 0.00161,019 0.01931 0.0180 0.00009 0.0021 0.00108 0.00131,020 0.04927 0.0209 * * 0.00051 0.0012 0.00001 0.00171,021 20.03729 0.0185 * * 0.00051 0.0021 0.00104 0.00161,022 0.00943 0.0192 0.00097 0.0008 0.00010 0.00171,023 0.01707 0.0201 20.00004 0.0022 0.00042 0.00101,024 20.00222 0.0226 20.00020 0.0022 20.00007 0.00171,025 20.00037 0.0193 0.00003 0.0022 0.00050 0.00161,026 0.00226 0.0187 0.00005 0.0021 20.00005 0.00161,027 20.01786 0.0196 20.00001 0.0022 0.00046 0.00161,028 0.01432 0.0173 20.00082 0.0014 0.00004 0.00131,029 0.00137 0.0201 20.00001 0.0022 20.00008 0.00171,030 0.01939 0.0199 20.00011 0.0022 20.00051 0.00161,031 20.02801 0.0174 0.00327 0.0014 * * 0.00255 0.0014 *

1,032 20.01441 0.0203 0.00103 0.0013 0.00025 0.00171,033 0.01852 0.0173 0.00175 0.0015 0.00021 0.00131,034 0.00511 0.0193 0.00069 0.0022 0.00083 0.00161,035 20.02168 0.0201 20.00022 0.0022 20.00061 0.00161,036 0.00594 0.0174 0.00152 0.0012 20.00081 0.00151,037 0.01605 0.0195 20.00042 0.0019 20.00024 0.00171,038 0.01939 0.0199 0.00068 0.0022 0.00096 0.00171,039 0.02591 0.0251 0.00019 0.0022 20.00002 0.00171,040 20.05606 0.0244 * * 20.00061 0.0022 0.00012 0.00171,041 0.01317 0.0172 0.00102 0.0009 20.00042 0.00161,042 20.06122 0.0176 * * 0.00120 0.0017 0.00008 0.00151,043 20.04584 0.0183 * * 0.00098 0.0009 0.00005 0.00171,044 20.00331 0.0196 20.00002 0.0022 0.00024 0.00161,045 20.01086 0.0189 0.00006 0.0022 20.00047 0.00081,046 20.00346 0.0203 0.00005 0.0022 0.00077 0.00161,047 0.00825 0.0209 20.00094 0.0020 20.00002 0.00171,048 0.01976 0.0211 0.00002 0.0022 20.00005 0.00161,049 20.00989 0.0199 0.00137 0.0011 20.00002 0.0017

(continued )

Table V.Empirical BLUPs for therandom effects

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Intercept, b0i Pre-winning slope, b1i Post-winning slope, b2i

Bidder Estimate Std. Error Estimate Std. Error Estimate Std. Error

1,050 0.00875 0.0173 20.00241 0.0017 20.00032 0.00131,051 20.00641 0.0223 20.00076 0.0022 20.00003 0.00171,052 20.02699 0.0192 20.00020 0.0019 0.00025 0.00171,053 20.02850 0.0175 0.00174 0.0011 0.00151 0.00161,054 20.03086 0.0187 20.00202 0.0018 0.00045 0.00171,055 0.01323 0.0189 0.00001 0.0022 20.00052 0.00161,056 20.02446 0.0190 20.00018 0.0022 0.00077 0.00151,057 0.04773 0.0175 * * 20.00120 0.0020 20.00102 0.00141,058 0.02138 0.0167 0.00170 0.0019 20.00209 0.0007 * *

1,059 20.01648 0.0179 20.00311 0.0017 * 20.00101 0.00161,060 0.03425 0.0207 0.00025 0.0017 20.00005 0.00171,061 0.01487 0.0222 20.00003 0.0022 20.00002 0.00171,062 0.00531 0.0211 20.00001 0.0022 20.00017 0.00161,063 20.00409 0.0251 20.00004 0.0022 0.00007 0.00171,064 20.00129 0.0205 20.00002 0.0022 20.00024 0.00171,065 0.01476 0.0221 0.00068 0.0021 0.00006 0.00171,066 0.01847 0.0208 20.00064 0.0018 0.00007 0.00171,067 0.01789 0.0211 0.00010 0.0022 0.00021 0.0016

Notes: *Significant at p , 0.10; * *significant at p , 0.05 Table V.

Figure 3.

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especially for post-winning period. It therefore seems that Bidder 1,031 biddingstrategy before and after a winning bid is rather unpredictable.

DiscussionThis piecewise mixed effects analysis has focussed on the evaluation of the impact ofan “event” of interest – a wining bid – by identifying the specific types of biddingtrends with parameter estimates before and after a winning bid. In considering thefixed effects (i.e. the population mean effects), it clearly demonstrates the statisticalsignificance of the pre- and post-winning bidding trends. There is obviously arelationship between bid price (mark-up) and bidding success. The results show thatthe bidders in general bid low for time periods before a winning bid and they are lesscompetitive in time periods after a winning bid. This predicted population meanbidding trends for pre- and post-winning time periods are similar to McCaffer andPettitt’s (1976) cusum curve, confirming their observation on two types of biddingbehaviour, i.e. contractors would have a reasonable share of high and low bids over aperiod of time. This strengthens the notion that systematic changes in biddingbehaviour over a period of time do occur in reality at which the variations in bids canbe explained by changes in firm capacity level.

Considering the subject-specific effects that relate to differences in bidding trends, itis shown that these effects cannot be removed by simply considering the fixed effectsonly. The inappropriateness of the predicted population mean BCR profile forstatistical inference on individual bidders’ BCR profiles is well-demonstrated in theillustrative plot (Figure 3). In fact, the empirical BLUPs and the illustrative plot makethe empirical results here of especial importance, as they show not only thepredictability of subject-specific effects in response to the predictor variables, but alsorelative magnitude of the predicted individual bidders’ mean BCR profiles. Theevidence is suggestive that there is remarkable heterogeneity among bidders indecision making for pricing before and after a winning bid (which is reflected in thevarying individual bidders’ intercepts and slopes). The heterogeneity captures theindividual bidder characteristics, which may include its firm size, its competitivestrategy, and its capacity level (both utilised and unutilised) at the time of bidding. It isnoted that recent studies by Oo et al. (2007a, 2008, 2010a) have also detected theexistence of heterogeneity across bidders in modelling contractors’ bidding behaviour.

Here, insight into how individual bidders vary their bidding strategies in relation toa bidding success could be gained. Indeed, the proposed model has many potential usesfor competitor analysis in construction bidding, for example, it could be used todifferentiate the less competitive bidders from the more competitive, and to estimatethe probable range of competitors’ bids before and after a winning bid. The illustrativeplot is also useful in identifying key competitor(s) with highly competitive biddingtrend, even after a winning bid (e.g. Bidder 1,001).

ConclusionThis paper aims to provide an understanding on the process of changes in the price ofbuilding work before and after a winning bid – the “event” of interest in this study. Wehave studied the specific types of bidding trends for pre- and post-winning timeperiods using a piecewise mixed effects model. The bids analysed comprised thelongest series of bids with a winning bid in between, recorded from 67 Hong Kong

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contractors. In modelling the impact of a winning bid, the variations in bids areexpressed as a function of time relative to winning bid. In this way, the piecewisemixed effects model provides two separate sets of parameter estimates representingthe periods before and after a winning bid. In addition, the individual bidders’characteristics that relate to differences in bidding competitiveness have beenconsidered by introducing random (individual-specific) effects in the model.

The results show that there is a relationship between bid price (mark-up) andbidding success. The predicted population mean bidding trend shows that the biddersin general bid low for time periods before a winning bid and they are less competitivein time periods after a winning bid. Thus, the hypothesised bidding trend where“winning bids are preceded by increasingly more competitive bids, which will then befollowed by less competitive bids” is supported. This provides strong empiricalevidence for the need to incorporate firm capacity levels in the future development of asuitable theoretical framework on construction bidding. In examining theindividual-specific effects further though, it is shown that, the predicted meanbidding trends of individual bidders differ from the population mean trend to varyingdegrees. This indicates that there is remarkable heterogeneity among bidders indecision making for pricing before and after a winning bid, reflecting the differentcapacity levels of contractors concerned at the time of bidding.

Considering the limitations of this study, it is recognised that additional insight onthe impact of winning bids could be gained by considering multiple series of bids fromeach bidder. Although our approach uses only a single longest series of bids from eachbidder, it allows the estimation of pre- and post-winning bidding trends over a lengthybidding attempt. Future modelling attempt could also consider using contractsequence in date order to examine the magnitude of changes in pre- and post-winningbidding trends as a function of time. Another limitation is that other variables that mayinfluence the bidding trends before and after a winning bid have not been considered inthis study. For further work, the developed model can readily be extended toaccommodate other variables by adding parameters as fixed and/or random effects.Other bidding variables of diagnostic value include: firm size, firm capacity level andneed for work, availability of jobs, client identity, and bidding success rate. In fact, themodelling approach is very flexible and can accommodate a variety of study designsand hypotheses on the evaluation of the impact of a “critical” event in studies withrepeated measurements over time, for example, the impact of an economic shock (therecent global financial crisis) on contractors’ bidding behaviour. A longitudinal studyof construction firms’ growth could also apply the modelling approach in which the“event” could be a takeover or merger that may influence firm growth.

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Corresponding authorBee Lan Oo can be contacted at: bee.oo@sydney.edu.au

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