an econometric analysis of factors determining contractors' interest in public tenders

12
ECONOMISCHE SECTlE An econometric analysis of factors determining contractors’ interest in public tenders *) by E. Bakker **) U.D.C. 5 19.26/.27: 625.7/.8 (492) Samenvatting Het artikel behandelt de bepalende factoren van de belangstelling van aannemers voor openbare aanbestedingen in Nederland in 1957. De factoren, die in beschou- wing zqn genomen zqn: de grootte van het werk als kwantitatieve factor en de tgd van het jaar, de aard van het werk en de opdrachtgever als kwalitatieve factoren. Met kleinste kwadraten is het regressie-verband bepaald van het aantal deelnemers aan een aanbesteding (belangstelling) en de logarithme van de inschr@som van de laagste inschrqver (grootte van het werk); als de omvang van het werk het tien- voudige is neemt het aantal deelnemers met gemiddeld 3 d 4 toe. De onverklaarde residuen zyn geanaliseerd naar de directe en interactie-eflecten van de kwalitatieve factoren. Met behulp van gewogen kleinste kwadraten is de kwantitatieve invloed van de voornaamste effecten geschat. De gegevens over de aanbestedingen zgn ontleend aan Cobouw en hebben betrekking op 1416 aanbestedingen in de sectoren grondwerk en wegenbouw . 1. Introduction This article deals with the factors determining contractors’ interest in public tenders as measured by the number of participants in such tenders in The Netherlands in 1957. That year is particularly interesting because of the govern- ment’s decision to reduce public expenditure in view of the over-employment and the sizable deficit on the balance of payments prevailing at the end of 1956. One of the consequences of this decision was that the number of contractors participating in public tenders increased, since they feared the prospect of idle capacity. This effect took place gradually in the course of 1957 and it is therefore necessary to take account of it in the analysis which follows. Another deter- mining factor is the size of the object, since it is reasonable to assume that ceterisparibus there will be more interest in large objects than in small ones, on the average at least. A third factor is the nature of the work, such as earth work, road building, etc. Finally, there is the possibility that differences exist with respect to the organizers of the tenders (state, provincial, and municipal authorities, etc.). Out of the four factors mentioned, only one - the size of the object - is *) Report 6217, ECONOMETRW INSTITUTE, Netherlands School of Economics. **) The author thanks Prof. The i I for his help and suggestions by the preparation of this article. Statistica Neeriandica 17 (1963) nr. 2. 125

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Page 1: An econometric analysis of factors determining contractors' interest in public tenders

ECONOMISCHE SECTlE

An econometric analysis of factors determining contractors’ interest in public tenders *)

by E . Bakker **) U.D.C. 5 19.26/.27: 625.7/.8 (492)

S a m e n v a t t i n g Het artikel behandelt de bepalende factoren van de belangstelling van aannemers

voor openbare aanbestedingen in Nederland in 1957. De factoren, die in beschou- wing zqn genomen zqn: de grootte van het werk als kwantitatieve factor en de tgd van het jaar, de aard van het werk en de opdrachtgever als kwalitatieve factoren. Met kleinste kwadraten is het regressie-verband bepaald van het aantal deelnemers aan een aanbesteding (belangstelling) en de logarithme van de inschr@som van de laagste inschrqver (grootte van het werk); als de omvang van het werk het tien- voudige is neemt het aantal deelnemers met gemiddeld 3 d 4 toe. De onverklaarde residuen zyn geanaliseerd naar de directe en interactie-eflecten van de kwalitatieve factoren. Met behulp van gewogen kleinste kwadraten is de kwantitatieve invloed van de voornaamste effecten geschat. De gegevens over de aanbestedingen zgn ontleend aan Cobouw en hebben betrekking op 1416 aanbestedingen in de sectoren grondwerk en wegenbouw .

1. Introduction This article deals with the factors determining contractors’ interest in public

tenders as measured by the number of participants in such tenders in The Netherlands in 1957. That year is particularly interesting because of the govern- ment’s decision to reduce public expenditure in view of the over-employment and the sizable deficit on the balance of payments prevailing at the end of 1956. One of the consequences of this decision was that the number of contractors participating in public tenders increased, since they feared the prospect of idle capacity. This effect took place gradually in the course of 1957 and it is therefore necessary to take account of it in the analysis which follows. Another deter- mining factor is the size of the object, since it is reasonable to assume that ceterisparibus there will be more interest in large objects than in small ones, on the average at least. A third factor is the nature of the work, such as earth work, road building, etc. Finally, there is the possibility that differences exist with respect to the organizers of the tenders (state, provincial, and municipal authorities, etc.).

Out of the four factors mentioned, only one - the size of the object - is *) Report 6217, ECONOMETRW INSTITUTE, Netherlands School of Economics.

**) The author thanks Prof. The i I for his help and suggestions by the preparation of this article.

Statistica Neeriandica 17 (1963) nr. 2. 125

Page 2: An econometric analysis of factors determining contractors' interest in public tenders

clearly quantitative and the three others are qualitative. An obvious statistical method to handle this situation is covariance analysis, but in the present case there are at least two features which hamper its application. For one thing, three-way analysis of covariance requires a considerable number of observations and although the present number (1416) is larger than usual in econometric analysis, it is still not sufficiently impressive, partly also because there is a sizable residual variation. For another, the analysis of covariance in its usual form is based on the assumption of normally distributed disturbances, whereas our dependent variable (the number of participants) is constrained to be a positive integer. It was therefore decided to trace the separate effects of the qualitative factors and their interactions by means of a straightforward analysis of regression residuals. The procedure is explained in Sections 3-5 after the underlying data have been described in Section 2. Section 6 contains the final result in terms of a regression which contains separate additive effects for all qualitative variables and a limited number of first-order interactions.

2. Description of the data The analysis covers 1416 public tenders in 1957 which deal with earthwork

and road construction.l) The number of participants ranges from 1 to 41 with a mean of 11. The size of the object is measured by the lowest bid, which ranges from 5000 to 5 millions with a median of about 100,OOO (in guilders). To handle the effect of the government decision mentioned in Section 1 we divided the year 1957 into four quarters, which means that one of our qualitative factors is:

A . Time: A,. First quarter A,. Second quarter A,. Third quarter A,. Fourth quarter.

The second qualitative factor is:

Nature of the work: Earth work only Road construction only Combination of earth work and road construction Other combinations, i.e., earth work and/or road construction com- bined with a third category such as bridge or house building.

l) These are all public tenders in earthwork and road construction that have been published in the weekly journal C o b o u w.

Statistica Neerlandica 17 (1963) nr. 2. 126

Page 3: An econometric analysis of factors determining contractors' interest in public tenders

The third factor is: C. Organizer of the tender (the future proprietor of the work): C,. Municipal authorities C,. Provincial authorities (including polder boards, waterschappen) C,. National (R!'jkswatersraat) C,. Others: regional ad hoc committees, private companies, etc.

As a whole there are 64 combinations of qualitative factors, which will be indi- cated in the sequel by (A,B,C,), where the three indices take the values 1, . . ., 4.

3. The effect of the size of the object Let us indicate by N i j k ( t ) the number of participants in the tth public tender

which falls under the category (A$?jCk). The first part of the analysis consisted of tracing the effect of the size (S) of the object. After a number of graphical experiments and exploratory one-way covariance analyses it was decided to use the following specification :

which implies that the qualitative factors are constrained to have additive effects on the number of participants (possibly with appropriate interactions). Ordinary least-squares applied to grouped data - 59 observations each con- sisting of means of 24 original observations arranged according to increasing S-values - leads to

(3.2) N = - 4 . 8 8 7 + 3.243 log S, (1.64) (0.33)

which implies the following average N-values for some alternative sizes of the object:

(3.1) N a j k ( t ) == Olifk + lolog S i i k ( t ) f U i i k ( f ) ,

Size (in guilders) Average number of participants I0,Ooo 8

100,OOO 114 l , ~ , O o o 144

Figure 1 gives a picture of the regression (3.2) based on sample means of 48 observations each. It will be noted that this grouping procedure underesti- mates the residual variation, but the picture is sufficient to show that the semi- log specification is adequate.')

l) The coefficient of multiple correlation of the regression (3.2) is R = 0.795, the standard deviation of its residuals is s= 1.3 18. [There is of course the difficulty that there may be a speci- fication bias in estimating fl even when it is true that this coefficient is independent of i , j , k. For take the simple case in which there are only two combinations (iJ k) and let the first have a smaller constant term in (3.1) and also a smaller average of the independent variable than the second. In that case, as is easily seen from a simple graph, the Besthate is subject to an upward specification bias. We expect to come back to this in a later publication.]

Statistica Neerlandica 17 (1963) nr. 2. 127

Page 4: An econometric analysis of factors determining contractors' interest in public tenders

N 18

16

14

12

10

a

log s I

4 5 6

Fig.1

Regression of the number of participants in a public tender (N) on the ordinary logarithm of the lowest bid (log S).

4. The separate effects of the three qualitative factors We shall now write (3.2) in the more explicit form :

(4.1) Nijk(t) = 4.887 + 3.243 log Sij&(t) + vij&(f),

where the vij,(t) stand for least-squares residuals. These residuals will form the basis of the discussion in this section and the two which follow. For each combination (AiBjCk), the means

, (4.2)

are given in Table 1; the summation over f is over all cases falling under (AiBjCJ and nijk is the number of such cases. The table contains also the means

Statistica Neerlandica 17 (1963) m. 2. 128

Page 5: An econometric analysis of factors determining contractors' interest in public tenders

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Page 6: An econometric analysis of factors determining contractors' interest in public tenders

which are the average residuals for all combinations (A$+), (AiCk), (BjCk), respectively. Finally, the table specifies

i.e., the means of residuals for each Ai , each Bj, and each C,, respectively. In each cell the number of observations (ni jk , njj, = Zk nilk, n i . ., etc.) is added between brackets.

The first question to be settled is whether the variation of these average residuals around zero can be ascribed to chance. Take e.g. the mean of all residuals which fall under A,, viz., 5,. . = -2.33, which is based on n, . . = 364 observations. Now the standard deviation of the residuals of regression (3.2) is s = 1.318, which is based on sample means of 24 observations. In the present case we have 364 observations, so under classical least-squares conditions the standard error of 5,. . (when viewed as a random variable) is

1.318 x (24/364)* = 0.339, provided that there is no &effect. Evidently, the observed value Y,.. = -2.33 deviates too much from zero to be accounted for by random variability. If we go on in this way for A,, A,, . ., B,, . ., C,, . ., we conclude that this is generally the case. Accordingly the separate effects of these factors is estimated by the corresponding average residuals (rounded off to the nearest multiple of 4 in order not to suggest more accuracy than is really justified). These estimated effects are given in Table 2, from which we conclude that the number of par- ticipants gradually increased in the successive quarters of 1957 (the A-effect), that there is more interest in projects of a combined character than in projects dealing with either earth work or road construction alone (the B-effect), and that there is less interest in projects initiated at the state level than in those initiated by municipal or provincial authorities. The first feature (the A-effect) is essentially a corroboration of the remarks made at the beginning of Section 1. The second must presumably be ascribed to the fact that specialized projects tend to attract a limited number of specialized contractors, and the third to the fact that the RJhwuterstuut imposes rather severe requirements compared with local authorities.

TABLE 2. Estimated effects of the separate factors.

Index value (i,j, k ) I- I 1 2 3 4

Statistica Neerlandica 17 (1963) nr. 2. 130

Page 7: An econometric analysis of factors determining contractors' interest in public tenders

5. Analysis of interactions The simplest specification based on the results of Section 4 is

(5.1)

where A,, Bj, c k take the values specified in Table 2. If we would accept this, it would mean that the three qualitative factors are supposed to affect the dependent variable additively without any interaction. Obviously, it is inter- esting to test whether interaction exists or not. This can be done as follows. Ideally, Y i j k should be equal to A , + Bj + C , if there is no interaction; but the two quantities are random, so the only thing we can say is that the expectation of their difference vanishes. A suitable test statistic is therefore

Ni jk ( t ) = -4 .887 + A i + Bj + C k + 3.243 log S i j k ( t ) + residual

- ” i j k - (A i + B j f ck) -~ t . =

a j k 9

s i l k (5.2)

where sijk is the standard error of the difference. Now all components of the difference (Tiii , , A,, Bj, C,) are random, but since the number of observations on which Ai, Bj, C , are based ( n i . . , n .,., n a e k ) is generally much larger than that of Y i j k (viz., nijk) , we shall comfine ourselves to the random variation of i i j k . This leads to

(5.3) 24

s2.. -, 23 k

n i 3 k

where s = 1.318 is the estimated standard deviation of the disturbances of (3.2). In a completely analogous manner we define

72,. - (4 + 4). - i s . k - ( A a + t,j. = 9 t i . , - 9

s,j . si . k

(5.4) i . j k - ( B 3 $. c k )

‘ - 9 k =

Table 3 contains the ratios ti,,, f,, ., 1 , . k , t . j k and Fig. 2 gives the frequency distribution of the 64 values I , , , . If there would be no interaction, this distri- bution would have zero mean and unit variance, a t least approximately. Actually, the mean is 4 . 0 2 and the second moment around zero is 2.65, which means that there are at least some t’s which are too large in absolute value. Indeed, one quarter of the 64 t’s is 2 2 or _I -2. When looking at the two-factor combinations, ( A 2 E j ) , ( A , C k ) and (B3Ck), one is struck by the fact that (A,C,) has large t’s: t , ., = 4.84, t3.1 = -3.16, f a . , = -2.46. This sug- gests that C, (corresponding with municipal authorities) showed a relative

Statistica Neerlandica 17 (1963) nr. 2. 131

Page 8: An econometric analysis of factors determining contractors' interest in public tenders

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Page 9: An econometric analysis of factors determining contractors' interest in public tenders

-5 -4 -3 -2 -1 0, 1 2 3 4 Fig .2

frequency distribution of the standardized residues of the regression ofter eliminotion of the effects of seporote factors.

decline over time compared with the other categories. On comparing this with Table 2, which shows that C, has the largest positive effect out of all C’s, one is inclined to believe that the relative decline of C, must be due to the increased interest of contractors in other C’s which under normal circumstances do not attract a large participation. This presumption seems to be corroborated by the results of the (AiC3)-combinations. According to Table 2, C, (Rijkswuter- staat) has the largest negative effect; and Table 3 shows that the average residuals (corrected for the effects of Table 2) of (A&) increase over time with t3 .3 = 2.99 and t4.3 = 2.16. A further corroboration is supplied by B, with its positive effect in Table 2 and its decreasing average residuals for (AiB3) in Table 3.

If we introduce interactions for (Ail&), (A,C,) and (A&) this handles 11 of the 16 ratios tiln which are 2 2 in absolute value l). The remaining 5 all fall

l) “Handles” in the sense that there are 1 1 combinations (AiB,Ck) such that I tue 12 2 and (AdB,Ck) falls under (Ai&) or (A&) or (A&), e.g., (A,B,C1) which falls under (A,C,) and which has I,,, = 2.50.

Statistica Neerlandica 17 (1963) nr. 2. 133

Page 10: An econometric analysis of factors determining contractors' interest in public tenders

under C,, which is a “miscellaneous” group and must therefore be considered rather heterogeneous. There is hardly any regularity with respect to C, in Table 3 and the best way to handle this complication is by adjusting the residual variance.

6. A residual regression On the basis of the exploratory results of Section 5 we shall compute a

weighted regression which describes the i i i j k in terms of the three qualitative factors and their interactions. Since the separate effects of the individual factors require several coefficients, it is in order not to use too many coefficients to handle the interactions. Now we see in Table 3 that the corrected mean residuals for (A@3), (A&,) and (A&,) are all close to zero and that the differences between (A3B3) and (A4B3), between (A3C,) and (A4C1), and between (A3C3) and (A&,) are all rather small. These constraints will be imposed in our regression in the sense that “close to zero” and “rather small” is interpreted as zero. The regression then takes the following form :

- (6.1) V i j k = A , f Bj f c k + Di5 f E i k f E i j ~ ,

where the single-subscript symbols refer to separate factors, the double- subscript symbols to their interactions, and &i5k is a disturbance term. The A’s, B’s and C’s are constrained to have zero weighted average:

4 4 4

Zn,. . Ai = Zn.,. Bj = Zn.. k C, = 0. I 1 1

(6.2)

The D’s refer to the time - B3 interaction and are therefore zero for j # 3. More precisely:

(6.3) Di5 = 0 if j # 3 and if i = 2 D, = D4

where is put equal to zero because the corrected average residual for (A,B3) in Table 3 is so close to zero (see above) and OB = D , for similar reasons. The E’s refer to the time - C, and the time - C3 interactions and are therefore zero when k is neither 1 nor 3. More precisely:

E f k = O if 1 # k # 3 andif i = 2 (6.4) E.9, = 4,

E33 = Em,

see again the beginning of this section.

Statistics Neerlandica 17 (1963) nr. 2. 134

Page 11: An econometric analysis of factors determining contractors' interest in public tenders

Finally, the disturbances are taken as random variables with zero mean:

(6.5) Eeijk = 0, all i, j , k.

They are regarded as uncorrelated and to have variances which are inversely proportional to the number of observations on which the T i j k is based, except that in the cases j = 4, k # 4 and j # 4, k = 4 (heterogeneity with respect to either the nature of the work or the organizers of the tender) the variance is taken twice as large, while a fourfold variance is postulated for j = 4, k = 4 (“double” heterogeneity):

a02 var eijk = - if j # 4, k # 4 n i j k

2a,2 - if either j = 4 or k = 4

4aO2 ~ if both j = 4 and k = 4.

l’ij k

ni5 k

The estimation is then of the ordinary weighted least-squares type with 18 coefficients to be estimated. For the A’s we find:

A , A2 A3 A4 -2.65 4 . 6 3 1.55 2.03

(0.62) (0.41) (0.50) (0.46)

which is close to the preliminary results of Table 2. Contractors’ interest in public tenders increased during 1957 but at a decreasing rate towards the end of the period. For the B’s we obtain:

B1 B2 B3 8 4

(0.33) (0.35) (0.3 (1.3

0.11 -1.19 0.93 2.74

This is also close to the corresponding results of Table 2 except that the outcome for B3 is now lower; it will be remembered that B3 is one of the factors for which we introduced interaction. As far as point estimates are concerned it remains true that projects of a combined character (B3, B4) attract more interest than projects dealing with earth work (B,) or with road construction (B& only, but the present results suggest that there is significance only for B2 and B4. The results for the C’s are as follows:

c1 c2 c3 c‘l

(0.41) (0.60) (0.91) ( 0 . d

0.1 1 0.61 4 . 5 7 4 . 3 4

Statistica Neerlandica 17 (1963) nr. 2. 135

Page 12: An econometric analysis of factors determining contractors' interest in public tenders

Here again we find discrepancies compared with Table 2 for those C’s for which interaction is introduced. At the level of point estimates it remains true that contractors’ interest in projects of the RijksMqaterstaat is less than those of the municipal authorities, but the difference cannot claim to be significant. For the interaction terms, finally, the following results are obtained :

D,, D, = D,, E, I E31 = ‘41 4 3 Ea3 = E$$

( 1 . J (1.23) (1.19) (0.87) (1.26) (1.2,)

-0.0 1 0.62 3.50 --1.32 ---2.14 -4.07

Evidently, the standard errors are such that there is significance only in a limited number of cases. We may say with some confidence that there was more interest in municipal public tenders in the first quarter of 1957 than in the second. We may also say (but with less confidence) that the interest in municipal public tenders in the second half year was less and that the interest in projects of the national authorities in the first quarter was below that of later months. But we cannot say much more.

7. Conclusions The main conclusions can be summarized as follows: ( I ) The analysis, which deals with 1416 public tenders in The Netherlands

in 1957 in the field of earthwork and road construction, suggests a semi-log dependence of the number of participants in such tenders on the size of the object as measured by the lowest bid. It is estimated that when the size increases tenfold, the number of participants increases by 3 or 4 on the average.

(2) The number of participants increased gradually in the course of 1957, quite apart from the dependence of this number on the size of the object and the other determining factors which will be discussed below. On the average the difference in the numbers of participants in the first and the last quarter of 1957 is about 4 or 5. This development must be ascribed to the government’s decision to curtail public expenditure in this period, which induced contractors to expect idle capacity and therefore raised their interest in public tenders.

(3) There is some evidence that contractors show less interest in specialized objects (dealing with either earthwork or road construction alone) than in objects of a combined character. There is also some evidence that they showed less interest in public tenders organized by the national authorities than in those by local authorities, presumably because of the more severe requirements imposed by the former, and that this difference tended to decline in the course of the year because the prospect of idle capacity induced contractors to compete in markets where they normally expect few competitors.

Statistica Neerlandica 17 (1963) nr 2. 136