OWNERSHIP AND PRODUCTION COSTS*
Choosing between public production and
contracting out
Henry Ohlsson
Uppsala University, Sweden
March 1998
Abstract
Many comparisons of the performance of public and private producers use
a public/private ownership dummy variable to capture cost di¤erences in
cross section data. This is appropriate if the producer choice is random.
The dummy variable model is, however, logically inconsistent if the producer choice depends on cost di¤erences. If cost di¤erences do not matter
for choice, there is still a risk for selectivity bias if there are other variables
a¤ecting the producer choice. I compare public and private enterprises using refuse collection costs in 115 Swedish municipalities. The data cover 170
enterprises. First, I …nd that cost di¤erences do not a¤ect producer choice.
Second, producer choice is important for costs. Third, the cost advantage
found for private …rms using the dummy variable model disappears when
choice is taken into account. Fourth, the parameters of the cost functions
di¤er between private and public …rms.
Keywords: public ownership, private ownership, competitive tendering,
contracting out, cost minimization, switching regression model with endogenous switching, privatization
JEL 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 provided most of the data. Helpful comments and suggestions from Sören Blomquist and seminar
participants at Uppsala University are gratefully acknowledged.
1. Introduction
The discussion about the performance di¤erences between private and public enterprises, e.g., in the literature on privatization, clearly illustrates the di¢culties
to measure …rm performance.1 Private and public enterprises may di¤er in objectives. 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 if
there 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 and
public enterprises may di¤er in how managers are monitored or in the incentive
structure of managers. It is often conjectured that public enterprises will be less
e¢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 measure allocative and internal e¢ciency poorly when there is no competition. This is
an argument for using costs instead. Vining and Boardman (1992) is an extensive
survey of the empirical literature on the e¤ect of ownership on e¢ciency.2 The
survey includes, e.g., previous studies of the costs of garbage collection. Vining
and Boardman argue that ownership in itself has a separate role from the degree
of competition in the output market. Borcherding et al. (1982), on the other
hand, argue that there are no ownership e¤ects when controlling for competition.
Domberger and Jensen (1997) argue that the evidence shows that contracting out
may reduce costs considerably.
The starting point for this paper is that many previous studies of the performance of public and private enterprises use dummy variables to capture the
e¤ects of public/private ownership (or market organization in general) in cross
sections.3 A model speci…cation assuming (i) that there is a constant cost di¤erence between public and private production and (ii) that the choice of producer
1
See, e.g., Vickers and Yarrow (1988) and Bös (1991) for a discussion about privatization.
Szymanski and Wilkins (1993) and Szymanski (1996) are more recent studies of competitive
tendering in refuse collection in the UK.
3
There is also the question why garbage collection should be compulsory and publicly provided. What is the market failure? Consumption of collection services is rival and exclusion is
possible. However, externalities exist because individuals are jointly damaged by deteriorations
in the environment when some individuals choose low (or no) levels of collection services. The
deteriorations are characterized by indivisibilities and exclusion is di¢cult or impossible.
2
1
depends on the cost di¤erence gives rise to a model that is logically inconsistent
using the terminology of Maddala (1983).4 The dummy variable approach will be
appropriate 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. If
this is the case, the dummy variable model is misspeci…ed. It could also be that
other factors are important for the producer choice. But then important variables
are omitted with the dummy variable approach.5 This may result in selectivity
bias.
Instead a cost comparison …ts well in the framework of a switching regression
model with endogenous switching. The objective of the paper is to estimate of
model of this kind using Swedish data. The data set comes from a survey made
by the Swedish Competition Authority in 1989 covering the garbage collection
in 115 of Sweden’s 284 municipalities. In 56 municipalities, the collection was—
completely (35) or partly (21)—done by the local government. In the remaining
59 municipalities, private …rms were the sole collectors. All in all 150 ”…rms”
were involved, 55 public and 95 private. Some …rms, however, operated in more
than one municipality. The data are disaggregated to municipality level so the
number of …rms on municipality level is 170, 56 public and 114 private. There are
unfortunately many missing observations for the cost data. In most estimations
I can only use 47 public …rms and 76 private …rms. Appendix A presents more
information 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¤ecting
choice, e.g., the share of single family houses in the housing stock.
2. Producer choice is important for costs. Not taking choice into account will
result in selectivity bias when estimating cost functions.
3. The cost advantage found for private …rms using the dummy variable approach disappears when choice is taken into account.
4. The estimated parameters in the cost functions di¤er between private and
public …rms. The dummy variable speci…cation can, therefore, also be questioned because of this.
4
Heckman (1978) and Maddala and Lee (1976) discuss this.
Dubin and Navarro (1988, p. 219) ask: “. . . if private monopoly is the e¢cient, costminimizing alternative, why do over half of the local communities choose other forms of market
organization?”
5
2
The paper is organized as follows: In section 2, I discuss the potential problems
with the dummy variable approach. I also specify a more general model and
discuss how it should by estimated. The estimations of producer choice models
and 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 when
comparing public and private enterprise performance is to estimate a single cost
function with production quantity and factor prices as explanatory variables, and
simply adding a dummy variable for the type of ownership. In the o¢cial government report, using this data set, the costs in private garbage collection were
estimated to be 25 percent less than in public production. Reestimating the equation, adding housing density as explanatory variable, I get the results reported in
Table 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 housing
density 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 ownership
dummy 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 a
constant cost di¤erence between public and private production and (ii) that the
choice of producer depends on the cost di¤erence and a stochastic term, gives
rise to a model that is logically inconsistent. The problem can be illustrated as
follows. Suppose that we have a cost model:
C = ¯X + ®I + u;
(1)
where the vector X includes production quantity and factor prices, ®I captures the
ownership e¤ect (I = 1 for private), and u is an error term. The parameter ® < 0
if private production is cheaper. Moreover, suppose that there is a choice equation
saying 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 is
cheaper. 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 the
notation of (1) and (2)):7
6
I have used the LIMDEP version 7.0 software package throughout the paper, see Greene
(1995).
7
Heckman (1978, p. 936) also provides a proof of this proposition.
3
Table 1: Cost per ton, dummy variable models.
quantity
-0.11
(1.95)
-0.15
(2.74)
-0.22
(3.82)
pick-up points per ton
0.21
(3.06)
0.22
(3.51)
0.16
(2.64)
pick-up frequency
0.02
(0.25)
-0.02
(0.23)
-0.06
(0.64)
distance
0.16
(3.31)
0.13
(2.96)
0.14
(3.20)
wage rate
0.24
(1.97)
0.19
(1.65)
cost of capital
0.20
(1.96)
0.23
(2.32)
housing density
private ownership
0.09
(2.94)
-0.13
(1.22)
constant
-0.11
(1.17)
-0.19
(2.02)
-0.23
0.78
1.42
(0.59) (1.71) (2.89)
R2
0.19
0.28
0.33
SEE
0.49
0.43
0.41
RSS
27.56
19.96
18.48
log likelihood
-82.58 -62.57 -58.06
n of obs
123
117
117
Notes. All variables are in logs except the private
ownership dummy. Absolute t-values within
parentheses.
4
Lemma 1. Suppose I ¤ is an unobserved variable, with the corresponding observed variable I = 1 if I ¤ > 0 and I = 0 if I ¤ · 0. Then a model of the form
I ¤ = °Z + ±®I + À, where Z is a variable, and ° is a parameter, is logically
inconsistent 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 only
if ±® = 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 choice
to 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 public
and private enterprises to have di¤erent cost functions (di¤erent ¯s). This could
be because the production technologies di¤er. Suppose that our model is:
private costs: C1 = ¯1 X1 + u1;
(3)
public costs: C2 = ¯2 X2 + u2 ;
(4)
producer choice: I ¤ = °Z + ±(C1 ¡ C2) + À;
(5)
I ¤ = °Z + ±(¯1 ¡ ¯2 )X + ±(u1 ¡ u2 ) + À;
(6)
where À is an error term. This is a switching regression model with endogenous
switching. 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:
which can be given new parameters to become I ¤ = ° ¤ Z ¤ + À ¤ . The conditional
expected costs are:
E(C1jI = 1) = ¯1X + ¾1À
Á(° ¤Z ¤ )
;
©(° ¤ Z ¤)
Á(° ¤ Z ¤)
E(C2jI = 0) = ¯2X ¡ ¾2À
;
1 ¡ ©(° ¤ Z ¤)
8
(7)
(8)
The problem can be illustrated in deterministic form. Suppose that private production is
cheaper. Then private production should always be chosen and there would be no observations
of public production.
5
where Á(° ¤ Z ¤ ) and ©(° ¤ Z ¤) are the density function and the distribution function
of the standard normal evaluated at ° ¤ Z ¤. The parameters ¾1À and ¾2À are the
covariances between the error term in the choice equation (À) and the error terms
in the cost equations (u1 , u2 ). The correlation ¾1À can be expected to be negative
while ¾2À can be expected to be positive.
The switching regression model with endogenous switching, (3) - (5), can be estimated using full information maximum likelihood. Alternatively, the structural
probit method can be used. This approach has three steps:
1. Estimate the reduced form choice equation (6) using probit to get °^ ¤ . Compute Á(^
° ¤Z ¤ ) and ©(^
° ¤ Z ¤ ):
2. Estimate the selection models corresponding to (7) and (8) using 2SLS to
get ¯^ 1 , ¯^ 2 , ¾
^ 1À , and ¾^ 2À . Compute (C^1 ¡ C^2) = (¯^ 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 when
choosing to contract out. I will, however, for the moment assume that cost plus
contracts are used. I will also assume that there are no di¤erences in the possibilities for the public sector to forecast the costs of own production and the costs
when contracting out.
Second, I have found that there are systematic di¤erences in the input prices
paid 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 10-15
percent less for their trucks. As …rms cannot be assumed to be price takers, I do
not include factor prices in the cost models.
3. Costs and producer choice
This section presents what I have done. There are many missing observations for
the cost variables while the municipality level data I use in the choice models
are complete. There is, therefore, a potential sample selection problem. Table 2
reports 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 data
are available. The estimated coe¢cients do not di¤er considerably between the
two estimations. The share of single family houses in the housing stock seems to
be the most important variable for producer choice. Running a probit on whether
6
Table 2: Ownership choice, probit models.
private
ownership
=1
0.02
(0.09)
cost data
available
=1
0.19
(0.77)
private
ownership
=1
0.18
(0.65)
average income
1.61
(0.80)
-3.27
(1.78)
-0.07
(0.03)
population
-0.19
(0.53)
0.37
(1.27)
-0.61
(0.92)
population density
0.18
(0.04)
9.13
(1.55)
2.70
(0.40)
housing density
0.92
(0.09)
-16.7
(1.53)
-1.89
(0.15)
share of single family houses
2.50
(2.33)
0.75
(0.79)
2.83
(1.99)
2.85
(1.57)
-97.8
0.56
4.94
0.552
170
-1.29
(0.50)
-74.7
0.54
14.1
0.028
123
socialist
constant
-2.44
(1.17)
log likelihood
-102.0
avg likelihood
0.55
Â2
11.52
signi…cance level
0.074
n of obs
170
Notes. Absolute t-values within parentheses.
cost data are available does not give any particularly signi…cant coe¢cients, see
column 2. My conclusion is that the subsample is not biased. A Â2 -test of the
restriction that the model only has a constant does not reject the restriction.
Table 3 present estimations of cost functions with controls for sample selection
using 2SLS. The probit in Table 2, column 3 is used to compute the lambda
Á
variable which equals ©Á for private ownership and ¡ 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-up
points per ton is important for public costs, see column 1 and column 2. I have
calculated an F -test of the hypothesis that the output coe¢cient are the same
for private and public …rms. Column 3 reports a dummy variable estimation
for the whole sample, controlling for sample selection, with the restrictions on
7
Table 3: Cost functions, sample selection models.
private
ownership
-0.17
(1.91)
public
ownership
-0.05
(0.76)
all
all
-0.09
(1.52)
-0.11
(1.95)
pick-up points per ton
0.19
(1.92)
0.43
(5.06)
0.21
(3.16)
0.21
(3.06)
pick-up frequency
0.01
(0.05)
0.19
(1.28)
0.01
(0.05)
0.02
(0.25)
distance
0.23
(3.06)
0.05
(1.54)
0.16
(3.64)
0.16
(3.31)
0.74
(2.07)
-0.13
(1.22)
quantity
private ownership
lambda
-0.95
(2.31)
constant
0.37
(0.68)
R2
0.28
SEE
0.52
RSS
19.25
log likelihood
-55.66
n of obs
76
Notes. All output variables are in logs.
Absolute t-values within parentheses.
8
-0.06
(0.35)
-0.58
(2.63)
-1.08
(2.03)
0.52
0.23
2.08
6.58
47
-0.72
(1.66)
0.26
0.45
23.67
-73.19
123
-0.23
(0.59)
0.19
0.49
27.58
-82.58
123
output coe¢cients and on the lambda coe¢cient imposed. The F (5; 111)-statistic
is 2.44, which corresponds to a signi…cance level of 0.039. The hypothesis that the
coe¢cients are the same can be rejected at the 5 % level. A likelihood ratio test
of the restrictions gives a Â2 (5)-statistic with a value of 48.20, which corresponds
to 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 function
but not in the public. Both coe¢cients have the predicted signs. Davidson and
MacKinnon (1993) suggest 2SLS should be used to test for selectivity bias while
maximum likelihood estimation should be used if selectivity bias cannot be rejected. 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 sample
selection in column 3 can be compared with an estimation without controlling for
sample selection, see column 4. Most coe¢cients are very similar. The private
ownership dummy, however, is positive and borderline signi…cant when controlling
for sample selection while it is negative but insigni…cant not controlling for sample selection. Maximum likelihood estimation gives an insigni…cant and positive
dummy variable, see Appendix B. In other words, the cost advantage found for
private …rms using the dummy variable approach disappears when choice is taken
into account. It should be stressed that these two models are logically inconsistent
if cost di¤erences matter for choice.
Table 4 suggests that cost di¤erences do not matter for choice. Column 1
reports the estimation of a reduced form probit. The only signi…cant output
variable is quantity. I have computed excess private costs using the estimations
reported in Table 3 column 1 and column 2. A cost minimizing behavior would
imply 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¢cient
for excess private costs.
Column 3 of Table 4 repeats the choice probit from Table 2. A likelihood ratio
test of the restriction that excess private costs gives a Â2(1)-statistic with a value
of 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 choice
equation assuming that lower costs matter for choice. The maximum likelihood
estimations did not, however, converge or gave unreasonable results. I interpret
this as that this model speci…cation is not appropriate for the present data.
9
Table 4: Ownership choice taking costs into account, probit models.
reduced form
0.05
(0.17)
structural form
0.22
(0.81)
0.18
(0.65)
average income
3.61
(1.24)
0.09
(0.03)
-0.07
(0.03)
population
0.55
(0.53)
-0.67
(1.01)
-0.61
(0.92)
population density
8.05
(0.91)
2.60
(1.55)
2.70
(0.40)
housing density
-14.5
(0.87)
-1.46
(0.11)
-1.89
(0.15)
share of single family houses
1.82
(1.14)
2.89
(2.03)
2.83
(1.99)
socialist
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
(0.39)
log likelihood
-54.67
avg likelihood
0.64
Â2
54.28
signi…cance level
0.000
n of obs
123
Notes. Absolute t-values within parentheses.
10
-1.76
(0.67)
-74.04
0.55
15.54
0.030
123
-1.29
(0.50)
-74.74
0.54
14.13
0.028
123
4. Concluding remarks
Many comparisons of the performance of public and private producers use a public/private ownership dummy variable to capture cost di¤erences in cross section
data. This is appropriate if the producer is randomly chosen. The dummy variable model is, however, logically inconsistent if the producer choice depends on
cost di¤erences. If cost di¤erences do not matter for choice, there is still a risk for
selectivity bias if there are other variables a¤ecting the producer choice. I compare public and private enterprises using refuse collection costs in 115 Swedish
municipalities. 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¤ecting
choice, e.g., the share of single family houses in the housing stock.
2. Producer choice is important for costs. Not taking choice into account will
result in selectivity bias when estimating cost functions.
3. The cost advantage found for private …rms using the dummy variable approach disappears when controlling for sample selection.
4. The estimated parameters in the cost functions di¤er between private and
public …rms. The dummy variable speci…cation can, therefore, also be questioned because of this.
11
Appendix A. The data
Municipality level data
Socialist = 1 if the Social Democrats and the Left Party had a majority of the
seats in the municipality council 1987. Source: Statistics Sweden, Yearbook
for 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 Swedish
Municipalities 1987.
Population density, the number of inhabitants per square kilometer, 1 January
1987. Source: Statistics Sweden, Yearbook for Swedish Municipalities 1987.
Housing density, total number of housing units in the municipality 1985 divided
by 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 the
total number of housing units 1985. Source: Statistics Sweden, The 1985
Census.
Firm level data
The …rm level data are for 1987 and come from the survey by the Swedish Competition 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 Survey
Form B, question 1. I have divided the data with quantity.
Pick-up frequency. Data on number of pick-ups come the answers to Survey
Form B, question 1. I have divided the data with the number of pick-up
points.
Distance. Data for distance driven are in kilometers and come from Survey Form
B, question 7.
12
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 both
the municipality and the …rm have costs for collection within a certain area.
In these cases I have added the costs, but payments to contractors should
not be included.
Wage rate, wage costs divided by the number of employees. Wage cost data
including payroll taxes are in SEK and come from Survey Form D, line 6
and 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 cost
data are in SEK and come from Survey Form D, line 10 leasing costs, line
11 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 and
municipalities.
13
Appendix B. Maximum likelihood estimations
Table 1: Cost functions, sample selection models.
quantity
pick-up points per ton
pick-up frequency
distance
private ownership
-0.17
(1.72)
0.18
(1.82)
0.01
(0.02)
0.23
(2.73)
public ownership
-0.04
(0.49)
0.42
(5.93)
0.19
(1.25)
0.06
(1.51)
0.08
(0.07)
-1.10
(1.80)
private ownership
constant
socialist
-0.07
(1.15)
0.20
(3.44)
-0.03
(0.14)
0.15
(2.91)
0.09
(0.52)
-0.58
(0.77)
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
-158.16
n of obs
123
123
123
Notes. All output variables are in logs. Absolute t-values within parentheses.
14
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