OWNERSHIP AND PRODUCTION COSTS*Choosing between public production and

contracting out

Henry OhlssonUppsala University, Sweden

March 1998

Abstract

Many comparisons of the performance of public and private producers usea public/private ownership dummy variable to capture cost di¤erences incross section data. This is appropriate if the producer choice is random.The dummy variable model is, however, logically inconsistent if the pro-ducer choice depends on cost di¤erences. If cost di¤erences do not matterfor choice, there is still a risk for selectivity bias if there are other variablesa¤ecting the producer choice. I compare public and private enterprises us-ing refuse collection costs in 115 Swedish municipalities. The data cover 170enterprises. First, I …nd that cost di¤erences do not a¤ect producer choice.Second, producer choice is important for costs. Third, the cost advantagefound for private …rms using the dummy variable model disappears whenchoice is taken into account. Fourth, the parameters of the cost functionsdi¤er between private and public …rms.Keywords: public ownership, private ownership, competitive tendering,contracting out, cost minimization, switching regression model with en-dogenous switching, privatizationJEL classi…cations: D24, E22, L32, L33

Correspondence to: Henry Ohlsson, Department of Economics, Uppsala University, Box 513,SE–751 20 Uppsala, Sweden, phone +46 18 471 10 96, fax +46 18 471 14 78, email henry.ohlsson@nek.uu.se

*The Swedish Competition Authority …nances the research and has also collected and pro-vided most of the data. Helpful comments and suggestions from Sören Blomquist and seminarparticipants at Uppsala University are gratefully acknowledged.

1. Introduction

The discussion about the performance di¤erences between private and public en-terprises, e.g., in the literature on privatization, clearly illustrates the di¢cultiesto measure …rm performance.1 Private and public enterprises may di¤er in objec-tives. Public enterprises may not exploit their market position (instead they, e.g.,may maximize social welfare) while pro…t maximizing private …rms may do so ifthere is not enough competition. With competition, on the other hand, private…rms will not be able to extract monopoly rents.

The assumption that costs are always minimized, for any produced quantity,can be relaxed using a principal-agent perspective. In this situation, private andpublic enterprises may di¤er in how managers are monitored or in the incentivestructure of managers. It is often conjectured that public enterprises will be lesse¢cient internally because of too low cost-reducing e¤orts of public managers.This results in slack or X-ine¢ciency (Leibenstein 1969). There may, therefore,exist a trade-o¤ between allocative e¢ciency in output markets, on the one hand,and internal e¢ciency, on the other.

When empirically comparing the performance of private and public enterprises,costs and pro…ts are the evaluation criteria most often used. However, pro…ts mea-sure allocative and internal e¢ciency poorly when there is no competition. This isan argument for using costs instead. Vining and Boardman (1992) is an extensivesurvey of the empirical literature on the e¤ect of ownership on e¢ciency.2 Thesurvey includes, e.g., previous studies of the costs of garbage collection. Viningand Boardman argue that ownership in itself has a separate role from the degreeof competition in the output market. Borcherding et al. (1982), on the otherhand, argue that there are no ownership e¤ects when controlling for competition.Domberger and Jensen (1997) argue that the evidence shows that contracting outmay reduce costs considerably.

The starting point for this paper is that many previous studies of the per-formance of public and private enterprises use dummy variables to capture thee¤ects of public/private ownership (or market organization in general) in crosssections.3 A model speci…cation assuming (i) that there is a constant cost di¤er-ence between public and private production and (ii) that the choice of producer

1See, e.g., Vickers and Yarrow (1988) and Bös (1991) for a discussion about privatization.2Szymanski and Wilkins (1993) and Szymanski (1996) are more recent studies of competitive

tendering in refuse collection in the UK.3There is also the question why garbage collection should be compulsory and publicly pro-

vided. What is the market failure? Consumption of collection services is rival and exclusion ispossible. However, externalities exist because individuals are jointly damaged by deteriorationsin the environment when some individuals choose low (or no) levels of collection services. Thedeteriorations are characterized by indivisibilities and exclusion is di¢cult or impossible.

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depends on the cost di¤erence gives rise to a model that is logically inconsistentusing the terminology of Maddala (1983).4 The dummy variable approach will beappropriate if the producer instead is randomly chosen.

If private …rms are more e¢cient, why do we observe public production at all?It could be that cost di¤erences matter but that production technologies di¤er. Ifthis is the case, the dummy variable model is misspeci…ed. It could also be thatother factors are important for the producer choice. But then important variablesare omitted with the dummy variable approach.5 This may result in selectivitybias.

Instead a cost comparison …ts well in the framework of a switching regressionmodel with endogenous switching. The objective of the paper is to estimate ofmodel of this kind using Swedish data. The data set comes from a survey madeby the Swedish Competition Authority in 1989 covering the garbage collectionin 115 of Sweden’s 284 municipalities. In 56 municipalities, the collection was—completely (35) or partly (21)—done by the local government. In the remaining59 municipalities, private …rms were the sole collectors. All in all 150 ”…rms”were involved, 55 public and 95 private. Some …rms, however, operated in morethan one municipality. The data are disaggregated to municipality level so thenumber of …rms on municipality level is 170, 56 public and 114 private. There areunfortunately many missing observations for the cost data. In most estimationsI can only use 47 public …rms and 76 private …rms. Appendix A presents moreinformation about the variables I use.

The main results are

1. Cost di¤erences do not seem to a¤ect producer choice. The municipalities,in other words, do not minimize costs. There are other variables a¤ectingchoice, e.g., the share of single family houses in the housing stock.

2. Producer choice is important for costs. Not taking choice into account willresult in selectivity bias when estimating cost functions.

3. The cost advantage found for private …rms using the dummy variable ap-proach disappears when choice is taken into account.

4. The estimated parameters in the cost functions di¤er between private andpublic …rms. The dummy variable speci…cation can, therefore, also be ques-tioned because of this.

4Heckman (1978) and Maddala and Lee (1976) discuss this.5Dubin and Navarro (1988, p. 219) ask: “. . . if private monopoly is the e¢cient, cost-

minimizing alternative, why do over half of the local communities choose other forms of marketorganization?”

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The paper is organized as follows: In section 2, I discuss the potential problemswith the dummy variable approach. I also specify a more general model anddiscuss how it should by estimated. The estimations of producer choice modelsand cost models can be found in section 3. Section 4 concludes.

2. Models and estimation strategy

How it usually has been done. The most common empirical approach used whencomparing public and private enterprise performance is to estimate a single costfunction with production quantity and factor prices as explanatory variables, andsimply adding a dummy variable for the type of ownership. In the o¢cial gov-ernment report, using this data set, the costs in private garbage collection wereestimated to be 25 percent less than in public production. Reestimating the equa-tion, adding housing density as explanatory variable, I get the results reported inTable 1.6

All parameters for the output variables are signi…cant at the 5 percent level,except for pick-up frequency. Factor prices are borderline signi…cant while housingdensity is signi…cant. Costs in private …rms are 11 - 19 percent lower than in public…rms depending on which other variables are included. The private ownershipdummy is borderline signi…cant in the estimation reported in column 3.

Why it may be wrong. A model speci…cation assuming (i) that there is aconstant cost di¤erence between public and private production and (ii) that thechoice of producer depends on the cost di¤erence and a stochastic term, givesrise to a model that is logically inconsistent. The problem can be illustrated asfollows. Suppose that we have a cost model:

C = ¯X + ®I + u; (1)

where the vectorX includes production quantity and factor prices, ®I captures theownership e¤ect (I = 1 for private), and u is an error term. The parameter ® < 0if private production is cheaper. Moreover, suppose that there is a choice equationsaying that the probability of contracting out depends on the cost di¤erence:

I¤ = ±®I + À; (2)

where À is an error term. We would expect the parameter ± < 0 if private ischeaper. If I¤ > 0 then I = 1, private is cheaper, if I¤ · 0 then I = 0.

However, Maddala (1983, p. 118) presents the following lemma (I use thenotation of (1) and (2)):7

6I have used the LIMDEP version 7.0 software package throughout the paper, see Greene(1995).

7Heckman (1978, p. 936) also provides a proof of this proposition.

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Table 1: Cost per ton, dummy variable models.

quantity -0.11 -0.15 -0.22(1.95) (2.74) (3.82)

pick-up points per ton 0.21 0.22 0.16(3.06) (3.51) (2.64)

pick-up frequency 0.02 -0.02 -0.06(0.25) (0.23) (0.64)

distance 0.16 0.13 0.14(3.31) (2.96) (3.20)

wage rate 0.24 0.19(1.97) (1.65)

cost of capital 0.20 0.23(1.96) (2.32)

housing density 0.09(2.94)

private ownership -0.13 -0.11 -0.19(1.22) (1.17) (2.02)

constant -0.23 0.78 1.42(0.59) (1.71) (2.89)

R2 0.19 0.28 0.33SEE 0.49 0.43 0.41RSS 27.56 19.96 18.48log likelihood -82.58 -62.57 -58.06n of obs 123 117 117Notes. All variables are in logs except the privateownership dummy. Absolute t-values withinparentheses.

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Lemma 1. Suppose I¤ is an unobserved variable, with the corresponding ob-served variable I = 1 if I¤ > 0 and I = 0 if I¤ · 0. Then a model of the formI¤ = °Z + ±®I + À, where Z is a variable, and ° is a parameter, is logicallyinconsistent unless ±® = 0.

The proof is as follows: Pr(I = 0) = 1¡ F (°Z) while Pr(I = 1) = F (°Z + ±®).The probabilities sum to one, 1¡ F (°Z) + F (°Z + ±®) = 1. But this holds onlyif ±® = 0.8

Suppose that we study logically consistent dummy variable models, i.e., ± = 0.Going back to our …rst model (°Z = 0), cost di¤erences play no role for the choiceto contract out. The choice, or rather the assignment, is random according to À.If instead other variables a¤ect choice (°Z 6= 0), estimating the cost model (1)without taking choice into account may give selectivity bias.

How it could be done. One way of resolving the inconsistency is to allow publicand private enterprises to have di¤erent cost functions (di¤erent ¯s). This couldbe because the production technologies di¤er. Suppose that our model is:

private costs: C1 = ¯1X1 + u1; (3)

public costs: C2 = ¯2X2 + u2; (4)

producer choice: I¤ = °Z + ±(C1 ¡ C2) + À; (5)

where À is an error term. This is a switching regression model with endogenousswitching. Suppose that the same variables a¤ect costs so that X1 = X2 = X.We will have use for the reduced form of the choice equation. It is:

I¤ = °Z + ±(¯1 ¡ ¯2)X + ±(u1 ¡ u2) + À; (6)

which can be given new parameters to become I¤ = °¤Z¤ + À¤. The conditionalexpected costs are:

E(C1jI = 1) = ¯1X + ¾1ÀÁ(°¤Z¤)

©(°¤Z¤); (7)

E(C2jI = 0) = ¯2X ¡ ¾2ÀÁ(°¤Z¤)

1¡ ©(°¤Z¤) ; (8)

8The problem can be illustrated in deterministic form. Suppose that private production ischeaper. Then private production should always be chosen and there would be no observationsof public production.

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where Á(°¤Z¤) and ©(°¤Z¤) are the density function and the distribution functionof the standard normal evaluated at °¤Z¤. The parameters ¾1À and ¾2À are thecovariances between the error term in the choice equation (À) and the error termsin the cost equations (u1, u2). The correlation ¾1À can be expected to be negativewhile ¾2À can be expected to be positive.

The switching regression model with endogenous switching, (3) - (5), can be es-timated using full information maximum likelihood. Alternatively, the structuralprobit method can be used. This approach has three steps:

1. Estimate the reduced form choice equation (6) using probit to get °¤. Com-pute Á(°¤Z¤) and ©(°¤Z¤):

2. Estimate the selection models corresponding to (7) and (8) using 2SLS toget ^1, ^2, ¾1À , and ¾2À. Compute (C1 ¡ C2) = (^1 ¡ ^

2)X.

3. Estimate the structural form choice equation (5) using probit to get ±.

There are two additional comments to be made with regard the model speci-…cation. First, it should also be borne in mind that productions costs in private…rms not necessarily are the same as the payment of the public sector whenchoosing to contract out. I will, however, for the moment assume that cost pluscontracts are used. I will also assume that there are no di¤erences in the possi-bilities for the public sector to forecast the costs of own production and the costswhen contracting out.

Second, I have found that there are systematic di¤erences in the input pricespaid by public and private …rms. In a previous study using the same survey,Ohlsson (1996), I found that private …rms, controlling for other factors, pay 10-15percent less for their trucks. As …rms cannot be assumed to be price takers, I donot include factor prices in the cost models.

3. Costs and producer choice

This section presents what I have done. There are many missing observations forthe cost variables while the municipality level data I use in the choice modelsare complete. There is, therefore, a potential sample selection problem. Table 2reports some probit estimation that address this problem.

Table 2, column 1 is an ownership probit for the full sample of 170 …rms.Column 3 is a corresponding probit for the sample of 123 …rms for which cost dataare available. The estimated coe¢cients do not di¤er considerably between thetwo estimations. The share of single family houses in the housing stock seems tobe the most important variable for producer choice. Running a probit on whether

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Table 2: Ownership choice, probit models.

private cost data privateownership available ownership

= 1 = 1 = 1socialist 0.02 0.19 0.18

(0.09) (0.77) (0.65)

average income 1.61 -3.27 -0.07(0.80) (1.78) (0.03)

population -0.19 0.37 -0.61(0.53) (1.27) (0.92)

population density 0.18 9.13 2.70(0.04) (1.55) (0.40)

housing density 0.92 -16.7 -1.89(0.09) (1.53) (0.15)

share of single family houses 2.50 0.75 2.83(2.33) (0.79) (1.99)

constant -2.44 2.85 -1.29(1.17) (1.57) (0.50)

log likelihood -102.0 -97.8 -74.7avg likelihood 0.55 0.56 0.54Â2 11.52 4.94 14.1signi…cance level 0.074 0.552 0.028n of obs 170 170 123Notes. Absolute t-values within parentheses.

cost data are available does not give any particularly signi…cant coe¢cients, seecolumn 2. My conclusion is that the subsample is not biased. A Â2-test of therestriction that the model only has a constant does not reject the restriction.

Table 3 present estimations of cost functions with controls for sample selectionusing 2SLS. The probit in Table 2, column 3 is used to compute the lambdavariable which equals Á

©for private ownership and ¡ Á

1¡© for public ownership.Private and public costs functions seem to di¤er with respect to which output

variables are important. Distance is important for private costs while pick-uppoints per ton is important for public costs, see column 1 and column 2. I havecalculated an F -test of the hypothesis that the output coe¢cient are the samefor private and public …rms. Column 3 reports a dummy variable estimationfor the whole sample, controlling for sample selection, with the restrictions on

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Table 3: Cost functions, sample selection models.

private public all allownership ownership

quantity -0.17 -0.05 -0.09 -0.11(1.91) (0.76) (1.52) (1.95)

pick-up points per ton 0.19 0.43 0.21 0.21(1.92) (5.06) (3.16) (3.06)

pick-up frequency 0.01 0.19 0.01 0.02(0.05) (1.28) (0.05) (0.25)

distance 0.23 0.05 0.16 0.16(3.06) (1.54) (3.64) (3.31)

private ownership 0.74 -0.13(2.07) (1.22)

lambda -0.95 -0.06 -0.58(2.31) (0.35) (2.63)

constant 0.37 -1.08 -0.72 -0.23(0.68) (2.03) (1.66) (0.59)

R2 0.28 0.52 0.26 0.19SEE 0.52 0.23 0.45 0.49RSS 19.25 2.08 23.67 27.58log likelihood -55.66 6.58 -73.19 -82.58n of obs 76 47 123 123Notes. All output variables are in logs.Absolute t-values within parentheses.

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output coe¢cients and on the lambda coe¢cient imposed. The F (5; 111)-statisticis 2.44, which corresponds to a signi…cance level of 0.039. The hypothesis that thecoe¢cients are the same can be rejected at the 5 % level. A likelihood ratio testof the restrictions gives a Â2(5)-statistic with a value of 48.20, which correspondsto a signi…cance level of 0.000. This test strongly rejects the restrictions.

The sample selection control lambda is signi…cant in the private cost functionbut not in the public. Both coe¢cients have the predicted signs. Davidson andMacKinnon (1993) suggest 2SLS should be used to test for selectivity bias whilemaximum likelihood estimation should be used if selectivity bias cannot be re-jected. Appendix B presents maximum likelihood estimations. The results are,in general, similar to those reported in Table 3.

The dummy variable estimation for the whole sample controlling for sampleselection in column 3 can be compared with an estimation without controlling forsample selection, see column 4. Most coe¢cients are very similar. The privateownership dummy, however, is positive and borderline signi…cant when controllingfor sample selection while it is negative but insigni…cant not controlling for sam-ple selection. Maximum likelihood estimation gives an insigni…cant and positivedummy variable, see Appendix B. In other words, the cost advantage found forprivate …rms using the dummy variable approach disappears when choice is takeninto account. It should be stressed that these two models are logically inconsistentif cost di¤erences matter for choice.

Table 4 suggests that cost di¤erences do not matter for choice. Column 1reports the estimation of a reduced form probit. The only signi…cant outputvariable is quantity. I have computed excess private costs using the estimationsreported in Table 3 column 1 and column 2. A cost minimizing behavior wouldimply that excess private costs had a negative coe¢cient in the choice equation.Column 2 in Table 4, however, reports an insigni…cant (and positive) coe¢cientfor excess private costs.

Column 3 of Table 4 repeats the choice probit from Table 2. A likelihood ratiotest of the restriction that excess private costs gives a Â2(1)-statistic with a valueof 1.40, which corresponds to a signi…cance level of 0.236. This test, therefore,does not reject the hypothesis that cost di¤erences do not matter for choice.

I have also tried to simultaneously estimate the cost models and the choiceequation assuming that lower costs matter for choice. The maximum likelihoodestimations did not, however, converge or gave unreasonable results. I interpretthis as that this model speci…cation is not appropriate for the present data.

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Table 4: Ownership choice taking costs into account, probit models.

reduced form structural formsocialist 0.05 0.22 0.18

(0.17) (0.81) (0.65)

average income 3.61 0.09 -0.07(1.24) (0.03) (0.03)

population 0.55 -0.67 -0.61(0.53) (1.01) (0.92)

population density 8.05 2.60 2.70(0.91) (1.55) (0.40)

housing density -14.5 -1.46 -1.89(0.87) (0.11) (0.15)

share of single family houses 1.82 2.89 2.83(1.14) (2.03) (1.99)

excess private costs 0.64(1.17)

quantity -1.10(4.38)

pick-up points per ton -0.51(1.81)

pick-up frequency -1.05(0.05)

distance 0.17(1.02)

constant 1.42 -1.76 -1.29(0.39) (0.67) (0.50)

log likelihood -54.67 -74.04 -74.74avg likelihood 0.64 0.55 0.54Â2 54.28 15.54 14.13signi…cance level 0.000 0.030 0.028n of obs 123 123 123Notes. Absolute t-values within parentheses.

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4. Concluding remarks

Many comparisons of the performance of public and private producers use a pub-lic/private ownership dummy variable to capture cost di¤erences in cross sectiondata. This is appropriate if the producer is randomly chosen. The dummy vari-able model is, however, logically inconsistent if the producer choice depends oncost di¤erences. If cost di¤erences do not matter for choice, there is still a risk forselectivity bias if there are other variables a¤ecting the producer choice. I com-pare public and private enterprises using refuse collection costs in 115 Swedishmunicipalities. The data cover 170 enterprises.

The main results are

1. Cost di¤erences do not seem to a¤ect producer choice. The municipalities,in other words, do not minimize costs. There are other variables a¤ectingchoice, e.g., the share of single family houses in the housing stock.

2. Producer choice is important for costs. Not taking choice into account willresult in selectivity bias when estimating cost functions.

3. The cost advantage found for private …rms using the dummy variable ap-proach disappears when controlling for sample selection.

4. The estimated parameters in the cost functions di¤er between private andpublic …rms. The dummy variable speci…cation can, therefore, also be ques-tioned because of this.

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Appendix A. The data

Municipality level data

Socialist = 1 if the Social Democrats and the Left Party had a majority of theseats in the municipality council 1987. Source: Statistics Sweden, Yearbookfor Swedish Municipalities 1987.

Average income, total factor income per inhabitant older than 20 years, 1987.Source: Statistics Sweden, Yearbook for Swedish Municipalities 1989.

Population, 1 January 1987. Source: Statistics Sweden, Yearbook for SwedishMunicipalities 1987.

Population density, the number of inhabitants per square kilometer, 1 January1987. Source: Statistics Sweden, Yearbook for Swedish Municipalities 1987.

Housing density, total number of housing units in the municipality 1985 dividedby the area of the municipality. Sources: Statistics Sweden, The 1985 Census(housing units) and Yearbook for Swedish Municipalities 1987 (area).

Share of single family houses, the number of single family houses divided by thetotal number of housing units 1985. Source: Statistics Sweden, The 1985Census.

Firm level dataThe …rm level data are for 1987 and come from the survey by the Swedish Com-petition Authority (formerly the Swedish National Price and Cartel O¢ce).

Quantity. Data are in tons and come from the answers to Survey Form E,question 2.

Pick-up points per ton. Data on pick-up points come the answers to SurveyForm B, question 1. I have divided the data with quantity.

Pick-up frequency. Data on number of pick-ups come the answers to SurveyForm B, question 1. I have divided the data with the number of pick-uppoints.

Distance. Data for distance driven are in kilometers and come from Survey FormB, question 7.

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Costs. Data are in SEK per ton and come from Survey Form D, line 6-21 costs +line 22-24 depreciation - line 19 payments to contractors. Sometimes boththe municipality and the …rm have costs for collection within a certain area.In these cases I have added the costs, but payments to contractors shouldnot be included.

Wage rate, wage costs divided by the number of employees. Wage cost dataincluding payroll taxes are in SEK and come from Survey Form D, line 6and line 7. Data on the number of employees (full-time full-year equivalents)are from Survey Form B, question 4.

Cost of capital, vehicle costs divided by the number of vehicles. Vehicle costdata are in SEK and come from Survey Form D, line 10 leasing costs, line11 repairs and fuel, line 13 insurance, line 14 taxes, line 22 depreciation.Data on the number of vehicles are from Survey Form B, question 7.

Private ownership. Data are from the list of identi…cation codes of …rms andmunicipalities.

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Appendix B. Maximum likelihood estimations

Table 1: Cost functions, sample selection models.

private ownership public ownershipquantity -0.17 -0.04 -0.07

(1.72) (0.49) (1.15)pick-up points per ton 0.18 0.42 0.20

(1.82) (5.93) (3.44)pick-up frequency 0.01 0.19 -0.03

(0.02) (1.25) (0.14)distance 0.23 0.06 0.15

(2.73) (1.51) (2.91)private ownership 0.09

(0.52)constant 0.08 -1.10 -0.58

(0.07) (1.80) (0.77)

socialist 0.03 0.10 0.24(0.11) (0.34) (1.06)

average income 0.58 0.07 -1.66(0.22) (0.02) (0.56)

population -1.30 -0.88 -0.06(1.58) (1.16) (0.12)

population density -1.67 1.28 3.28(0.21) (0.14) (0.32)

housing density 7.89 1.46 1.16(0.52) (0.09) (0.23)

share of single family houses 2.34 2.23 1.16(1.63) (1.50) (0.89)

constant -1.34 -0.96 1.06(0.46) (0.31) (0.35)

¾ 0.64 0.24 0.60(5.86) (3.73) (10.2)

½ -0.71 0.40 0.82(2.69) (0.53) (7.10)

log likelihood -135.39 -71.30 -158.16n of obs 123 123 123Notes. All output variables are in logs. Absolute t-values within parentheses.

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