1

REVISITING THE PORTER HYPOTHESIS: AN EMPIRICAL ANALYSIS

OF GREEN INNOVATION FOR THE NETHERLANDS

George van Leeuwen (CBS) and

Pierre Mohnen (Maastricht University and UNU-MERIT)

April 28, 2015

Abstract

Almost all empirical research that has attempted to assess the validity of the Porter hypothesis

has started from reduced-form models, e.g. single-equation models for estimating the contribu-

tion of environmental regulation to productivity. This paper follows a structural approach that

allows testing what is known in the literature as the “weak” and the “strong” version of the

Porter hypothesis. Our “Green Innovation” model includes three types of eco-investments to

explain differences in the incidence of two types of eco-innovation, which are allowed to affect

labor productivity. We allow for complementarity between the two types of eco-innovations.

Using a comprehensive panel of Dutch manufacturing firm-level data we estimate the relative

importance of environmental regulations on eco-investment and eco-innovations. The results

of our analysis show a strong corroboration of the weak and a nuanced corroboration of the

strong version of the Porter hypothesis.

Keywords: Porter hypothesis, green innovation, environmental regulation, complementarity,

productivity.

JEL codes: H23, L5, O32, O38, Q55

Previous versions of the paper were presented at the FEMES conference in Singapore, and at

seminars/workshops at the Global Green Growth Institute in London, Brighton, Hangzhou,

Chengdu, Beijing, Pamplona, The Hague, Nice and the three workshops in preparation to this

special issue. We thank all participants for their critical remarks.

2

1. Introduction

The relationship between technological change and environmental policy has received a

lot of attention from scholars and policymakers during the last decades. This is partly because

the environmental consequences of social and business activity are affected by the rate and

direction of technological change, and partly because environmental policies may create new

constraints as well as new incentives that may shape the path of future technological develop-

ment (Jaffe et al., 2003).

Environmental technological progress is a very broad phenomenon and every description

of it cannot be more than very incomplete. Some examples concern 1) technologies that reduce

pollution at the end-of-pipe, such as scrubbers for use on industrial smokestacks or catalytic

converters for automobiles 2) technologies that increase user value for consumer products (e.g.

medicines) by introducing new production methods that use materials that are less harmful for

the environment and 3) implementation of technologies that are targeted to changes in produc-

tion processes that improve energy efficiency.

Environmental regulations (ER) in the form of carbon taxes, cap and trade or environ-

mental standards have been put in place to solve two market failures: the lack of environmental

innovations that have positive spillover effects on other firms just like any other kind of inno-

vation and the negative spillover effects in the form of water and air pollution, noise, climate

change, and non-renewable energy depletion connected to industrial activity. Let alone, firms

innovate too little especially in environmental technologies (see e.g. Jaffe et al., 2002,

Desrochers, 2008 and Cerin, 2012).

Opponents to these environmental regulations argue that they increase costs and reduce

the firms’ competitiveness. The Porter hypothesis (PH) asserts that polluting firms can benefit

from environmental policies, arguing that well-designed and stringent environmental regulation

3

can stimulate innovations, which in turn increase the productivity of firms or the product value

for end users (Porter, 1991; Porter and van der Linde, 1995). The claim is that there is no trade-

off between economic growth and environmental protection but a win-win situation instead.

Environmental regulation would benefit both society and regulated firms by triggering dynamic

efficiency, and these benefits may partially or fully offset the costs of complying with environ-

mental restrictions.

As argued by Kriegel and Ziesemer (2009), the central issue behind the testing of the PH

is the question whether regulation drives innovation. This calls for a structural modeling ap-

proach in investing the contribution of environmental regulations on green investment and of

green investment on innovation and productive efficiency.1 We will embark on this task by

adopting a Green CDM (Crépon-Duguet-Mairesse, 1998) type of model, similar to the model

used by Lanoie, Laurent-Lucchetti, Johnstone and Ambec (2011), that allows testing what Jaffe

and Palmer (1997) called the “weak” version and the “strong” version of the PH, referring to

the effect of environmental regulations on respectively environmental innovations and eco-

nomic performance. A number of studies have found support for the weak version of the PH,

little corroboration, however, exists of the strong version of the PH (see Wagner (2003), Popp

et al. (2010), Ambec and Barla (2006), and Ambec et al. (2011) for extended reviews). This

paper tries to shed new light on the PH by using a rich unbalanced Dutch firm panel data set

constructed by matching firms from four different types of surveys.2

1 Green investment refers to investments aimed at reducing the environmental burden of production (see Kemp,

2011).

2 The terms eco, environmental and green innovation will be used interchangeably, indicating each time an inno-

vation with a lower detrimental impact on the environment.

4

The plan of the paper is as follows. In section 2 an overview of the literature is given.

Section 3 discusses the model used in the empirical application. Section 4 presents the data.

The results are presented and commented in section 5. Section 6 concludes.

2. Literature review

There is a vast body of literature devoted to appraise the seminal contributions of Porter

(1991) and Porter and van der Linde (1995). Originating primarily from empirical regularities

found in the analysis of cross-country differences in the stringency of environmental regulation

and economic performance, the Porter hypothesis has triggered a lot of research both theoretical

and empirical in nature. It has been criticized for being merely based on anecdotal stories and

for the lack of a sound theoretical basis (see Palmer et al., 1995, and Cerin, 2006).

Some research attempts to provide a theoretical underpinning of the PH. Mohr (2002)

argues that it is a feasible outcome if one allows for the possibility of endogenous technical

change. More recent theoretical contributions that link the environment to endogenous growth

are given in Acemoglu et al. (2012) and Gans (2012). Ambec and Barla (2002) raise the ques-

tion whether regulation is indeed needed for firms to adopt profit-increasing innovations, point-

ing to the first primitive of the PH, i.e. that firms systematically ignore opportunities for profit

increasing innovations, and that environmental regulations can motivate firms to capture “low

hanging fruit” offered by environmental challenges to their business. The literature of behav-

ioral economics offers several explanations for underinvesting in environmental innovations

(see examples in Ambec and Barla, 2006). Other studies have analyzed the interaction between

competition and innovation. A recent example is the introduction of organic pharmaceutical

products discussed in Constantatos and Hermann (2011). By avoiding the use of environmen-

tally damaging fertilizers there is less environmental burden as well as more user value created

because organic drugs are healthier. But a win-win situation between regulation and innovation

5

is not self-evident because of conjectural variations, consumer inertia or potential first-mover

disadvantages.

Another strand of research focuses on the second primitive of the PH, i.e. the assertion

that environmental regulations should be well-designed and stringent enough to be successful

also from an economic point of view. An assessment of the instruments of environmental reg-

ulation and a judgment of their effectiveness can be found in Wagner (2003). The myriad of

environmental instruments can best be understood by distinguishing between command and

control and market based regulations. The instruments that set emission limits and standards

fall into the first class and are often labeled “end-of-pipe” regulations. Environmental taxes and

tradable emission permits are examples of the second class of instruments. Environmental ef-

fectiveness can be defined as the ability to achieve a predefined environmental target. The gen-

eral view is that this definition is more appropriate for the first class of instruments. By contrast,

the second class of instruments has a higher economic profile, because they are aimed at trig-

gering static and dynamic efficiency and internalizing environmental externalities.

Looking at the empirical evidence provided in the literature it can be concluded that the

picture is rather mixed. The number of papers and articles that have put the PH to the empirical

testing is overwhelming but they do not to lead to a general consensus. Much of this has to do

with the different research strategies and the availability of data. Compared to empirical evi-

dence at the macro or industry level, the number of papers that use firm level data is rather

scarce. Besides that, research is targeted at different measures of performance.

Cutting through different reviews of the empirical work testing the Porter hypothesis, it

can be concluded that many studies investigate the impact of environmental regulation on

productivity or productive efficiency in a reduced form estimation approach and that the em-

pirical evidence is mostly at the macro or industry level. In many cases this type of research

leads to the conclusion that environmental regulation has a negative impact on productivity.

6

This conclusion can be easily understood, because regulation forces firms to invest in the envi-

ronment and doing so increases production costs. If these investments do not lead to the renewal

of production processes then there is no reason for expecting substantial gains in resource effi-

ciency. There is, however, a measurement issue. “End-of-pipe” investments may reduce pollu-

tion but this reduction is not accounted for in output. The same capital and other inputs produce

two types of output: bad and good output and it is hardly possible to value the contribution of

(reducing) bad output. This raises serious problems when investigating the relation between

environmental regulation and (productive) efficiency.3 An interesting solution to circumvent

this problem is presented in Domazlicky and Weber (2004) and Weiss (2015). They use data

on toxic releases as bad outputs together with traditional output measures such as real value

added in a non-parametric analysis to identify technical change from efficiency change. Doma-

zlicky and Weber (2004) conclude that regulation has a negative impact on total factor produc-

tivity (TFP). Weiss (2004) finds that Swedish environmental regulations does not affect con-

ventional TFP growth but well green TFP growth in the Swedish pulp and paper industry.4

More interesting is the research that looks into the impact of environmental regulation on

innovation. Notable examples of this type of research can be found in several papers based on

the Mannheim Innovation Panel. The focus of research stretches from regulation driven inno-

vation alone (Rennings and Rexhäuser, 2010) to the impact of regulation driven innovation on

competitiveness (Rennings and Rammer, 2010), employment dynamics (Horbach and Ren-

nings, 2012) or profitability (Rexhäuser and Rammer, 2014). Support for the PH is provided by

concluding that environmental regulation does not harm competitiveness (Rennings and Ram-

mer, 2010) and that the contribution of regulation induced innovation to profitability is larger

3 This problem is well recognized by statisticians and environmental accounting is an important avenue for Na-

tional Accounts. See Muller et al. (2011) for a recent contribution to this problem. 4 The method used is the “directional output distance approach” developed by Chung et al. (2007) for constructing

the Malmquist-Luneberger index to decompose (changes in) TFP.

7

than the contribution of other (more) voluntary innovations (Rexhäuser and Rammer, 2014).

On data from the Swedish pulp and paper industry Weiss (2015) finds confirmation of the nar-

row version of the Porter hypothesis.

Ideally, a thorough empirical testing of the PH would rely on data of particular types of

regulations that would trigger innovations at the firm level. The most recent edition of CIS

contains new questions on environmental innovation. However, for the Netherlands, this new

module cannot be used to identify the role of different instruments of environmental regulation

properly. The only variable available on regulation in this research concerns firm responses to

environmental regulation in general, either existing or anticipated regulations. By contrast, the

German CIS allows a distinction between types of environmental regulations. After matching

the firm responses with external data on the age of regulations, Rennings and Rexhäuser (2010)

also investigated the long-term impact of different types of regulation on the adoption of envi-

ronmental innovation. Surprisingly they find that command and control regulations of the end-

of-pipe type can stimulate certain types of long-term innovation.

3. A Green CDM model

The empirical model used in this paper is a modified version of the so-called “CDM

model” (following the initials of Crépon, Duguet and Mairesse, 1998). A graphical presentation

of our model is given in Figure 1.5 The upper part of the figure points to the investment decision

stage. In the traditional CDM model this concerns the decision on how much to invest in R&D.

In this paper we face another investment decision problem, i.e. namely how much to invest in

order to reduce the environmental burden of the firm’s operations. The second block of the

model describes the green innovation function with eco-R&D and other eco-investments as an

5 The figure is an adapted version of the one presented in Crépon, Duguet and Mairesse (1998).

8

input and eco-innovations, possibly of different kinds, as outputs. The third block examines the

link between innovation outputs and productivity as a measure of economic performance. We

shall now describe each block in detail.

a. The investment decisions

We consider three eco-investments (X1): 1) eco-R&D, 2) eco-investment in end-of-pipe

facilities, and 3) eco-investment that is “process integrated”, i.e. combined with the renewal of

the main production processes of the firm. For each type of investment, we assume that firms

first decide whether to invest or not and then choose the investment intensity. Firms will invest

in each of these types of investment if the latent value of investing (denoted by a *) exceeds

some threshold value . The decision to invest in X1, DX1, can be expressed as follows:

if , and

(1)

c

11

iDX 1111

*1 cZDX iii

9

if .

The vector Zi1 in (1) collects the variables that are assumed to determine the selection of firms

that invest in X1. Model (1) is extended with a set of equations that determine the level of in-

vestment intensity for each of the three types of eco-inputs. For example, for some type of eco-

investment, this yields

if , and

(2)

if

Models (1) and (2) are applied to each of the three types of eco-investments. Assuming a

bivariate normal distribution for and (and this for each specific type of eco-investment),

the system (1) - (2) is a Tobit type II selection model (Amemiya,1984).

Although we are dealing in each case with a general investment problem, one can imagine

that the three types of investment are rather distinct. The traditional view is that expenditures

on non-eco R&D have a higher economic profile, and that such expenditures are quite different

from eco-investment (including eco-R&D) when judged from the point of the strategies of the

firms. This is particularly the case if we compare eco-investment performed to comply with

“control type” environmental regulation with R&D that is aimed at developing new goods. Not

at least because of the difficulty of evaluating the output of “bad goods” or of “process inte-

grated” eco-investment, which by definition aims at reducing bad output and increasing re-

source efficiency, it is impossible to use standard capital and investment theory to derive formal

investment models. At least, we consider such an exercise beyond the scope of this research.

01

iDX 1111

*1 cZDX iii

111*11 iiii eXXX 1

1

iDX

01

iX .01 iDX

1

1e

10

We let both the decision to invest and the intensity of eco-investment be a function of the

size of the firm. Larger firms are expected to have greater means and incentives to invest in

eco-investments. It is less certain that the intensity is also affected by the size of the firm, but

we do not want to exclude a scale effect. Government can internalize the environmental exter-

nalities by imposing environmental levies or by taxing the price of energy. The environmental

levies in total environmental exploitation costs are provided in the ECF data set. Constructing

an energy price, and especially a marginal tax for energy, is feasible but would substantially

reduce the size of our sample. Therefore as an indirect measure of the incentive to save on

energy because of an energy tax we use the energy cost share in total cost in both equations.

We assume the relative size of the environmental levies to affect the decision to initiate eco-

investments but not the intensity of these investments as opposed to the energy cost share, which

we let affect both the decision to invest and the intensity of investment. In the intensity of

investment equation we also control for the presence of eco-subsidies, the relative price of in-

vestment and labor6, and for industry and time effects. Our central variable of interest, the im-

portance of environmental regulation (existing or anticipated), is inserted as an explanatory

variable in each equation. Whenever possible we use one-period lagged variables to minimize

the possibility of endogeneity.

b. Innovation output

The middle part of figure 1 indicates that eco-investment leads eco-innovation output. We

consider two types of eco-innovation output: pollution-reducing and resource-saving eco- in-

novations. We observe dichotomous variables indicating whether a certain innovation has been

adopted or not. The two types of innovation are likely to be interrelated in the sense that the

6 The investment deflator is specific to each type of investment but common for all firms in a given sector. The

price of labor, however, is firm specific and is obtained by dividing the cost of labor by the number of full-time

employees.

11

return to one innovation could depend on the adoption of the other one for reasons of comple-

mentarity or substitutability between them. It is well documented in the econometric literature

(see e.g. Heckman, 1978, Tamer, 2003, Lewbel, 2007) that the estimation of a bivariate probit

with endogenous dummy variables raises severe problems of identification. There can be no

solution (in which case the system is said to be incoherent) or multiple solutions (in which case

it is said to be incomplete). The empirical literature offers several solutions to this problem. In

general, these solutions boil down to imposing zero restrictions on the coefficients of some of

the binary endogenous explanatory variables or by relying on recursive or triangular systems,

in which one of the choices is assumed to be leading (see for a discussion of completeness and

coherency section 2 of Tamer (2003)). One way to avoid incoherency and incompleteness is to

start from a McFadden (1973) solution by considering a multinomial choice problem based on

a random utility model. This framework was proposed more recently by Lewbel (2007) and

applied by Miravete and Pernías (2006) and Kretschmer, Miravete and Pernías (2012).

12

Let the total utility (in this case profit) be

𝑉 = 𝑉(𝑦1, 𝑦2) = (𝛽1′𝑥1 + 𝛼12𝑦2 + 𝜀1)𝑦1 + (𝛽2

′𝑥2 + 𝛼21𝑦1 + 𝜀2)𝑦2. (3)

The dichotomous variables for the two types of innovation are given by 𝑦𝑖(𝑖 = 1,2). There are

in total four possible combinations of innovation choices yielding respectively the following

profit outcomes:

𝑉(0,0) = 0 (4a)

𝑉(0,1) = 𝛽2′𝑥2 + 𝜀2 (4b)

𝑉(1,0) = 𝛽1′𝑥1 + 𝜀1 (4c)

𝑉(1,1) = 𝛽1′𝑥1 + 𝛽2

′𝑥2 + (𝛼12 + 𝛼21) + 𝜀1 + 𝜀2. (4d)

The “complementarity parameters” 𝛼12and 𝛼21 are placed in parenthesis because only

their sum can be identified.7 If (𝛼12 + 𝛼21) > 0 , the two innovations are complements

(substitutes). The model is complete because (latent) profitability is specified for all possible

strategies and coherent because every strategy should have a latent profit that exceeds the profits

of all other strategies. As pointed out by Lewbel (2007), the difference with respect to the tra-

ditional multinomial choice framework is that we do not have a separate specification for

𝑉(1,1) such as 𝛽3′𝑥3. Instead we use (4d) derived from the model for the total latent profit

function. In the annex we give a more detailed account of the construction of the likelihood

function of the Lewbel model for somewhat more general model, a trivariate probit, of which

7 Notice that if the ij ’s are equal to zero, we are in the presence of a bivariate Probit model.

Methods for estimating such models are readily available (see Capellari and Jenkins (2003,

2006) and Train (2003)). The number of draws used to compute the maximum simulated like-

lihood is 50.

)0(

13

the bivariate is just a special case. The are random errors that are supposed to be jointly

normally distributed.

The profitability of pursuing a particular innovation depends on the adoption of the

other innovation modes, through the “complementarity parameter”, on the magnitude of the

three types of eco-investment - it is, indeed, interesting to find out which investments affect

which types of innovation – and on a vector of control variables: the size of the firm, a dummy

for innovation cooperation, a set of industry and time dummies and especially the environmen-

tal regulation dummy, which captures whether firms respond to either existing or anticipated

ER. Since the three eco-investment intensities are endogenous, we replace them by the condi-

tional predictions of their latent variables estimated in the first step. In essence, the coefficient

of environmental regulation provides a test of the weak version of the PH in the terminology of

Jaffe and Palmer (1997).

c. Production function

Finally, we investigate the strong version of the PH by relating ER to labor productivity

(LP) via the effects of innovation output on the TFP component of LP. We regress the log

of labor productivity on the log of the capital-labor intensity, the log of the material-labor in-

tensity and the log of employment that captures deviations from constant returns to scale. We

make the left over, TFP, depend on two innovation output dummies, one representing pollution-

reducing and the other one resource-saving environmental innovation. The former captures en-

vironmental innovations targeted at lower uses of energy or materials and can be seen as a form

of end-of-pipe eco-innovation, aiming just at reducing pollution but not at changing the pro-

duction technology at the same time. The latter captures environmental innovations targeted at

lower CO2 emissions, lower use of polluting materials, less pollution in the production process

si '

iy

14

and improvements in recycling, and can be considered as a deeper innovation that aims at curb-

ing pollution by improving the production technology itself. We also control for industry and

year dummies. Since the innovation output measures are endogenous, we instrument them by

the predicted latent innovation variables from stage 2 (see e.g. Wooldridge, 2002). As a robust-

ness check we also account for the endogeneity of the traditional inputs by instrumenting them

by their lagged values.

4. Data

We have constructed a comprehensive data set by linking manufacturing firm-level data

for 2000 – 2008 from three different surveys: 8

1) The Survey on Environmental Costs of Firms (ECF). This yearly survey covers the period

2000 – 2008 and beyond. This is one of the most important data sources for this research project.

The survey collects (amongst others) data on environmental current exploitation costs, environ-

mental subsidies, expenses on environmental R&D and two types of non-R&D environmental

investments: “end-of-pipe” eco-investments and those related to the renewing of production

processes (so-called “process integrated eco-investment”). Because this survey only collects

data for manufacturing, our empirical analysis will be restricted to this branch of the economy.

2) The Community Innovation Surveys (CIS) that during our period of interest were conducted

every two years, covering the periods 2002-2004, 2004-2006 and 2006-2008. This survey con-

tains data on the existence or anticipation of environmental regulation and about a number of

8 We could also have used the yearly Energy use Survey, which collects volume data on energy

consumption of different types. These could have been used to construct marginal energy prices

at the firm-level after linking them with the data on energy costs collected in the Production

Surveys. Unfortunately, because of the poor coverage when combined with CIS we would have

faced a considerable loss of data.

15

environmental innovation targets: the reduced use of materials and of energy per unit of output

(which we shall denote as resource-saving eco-innovations) and the reduced CO2 footprint, the

replacement of materials with less polluting and hazardous substitutes, the reduced soil, water,

noise and air pollution, and the recycled waste, water and materials (all four of which we shall

regroup under the heading of pollution-reducing eco-innovations).9 Respondents were also

asked whether they cooperated in innovation.

3) The Production Statistics Survey (PS). This yearly survey contains firm-level data on gross

output, turnover, value added, intermediate inputs, replacement investment and the total energy

costs. If the depreciation rate is constant, replacement investment can serve as a proxy for cap-

ital stock.

9 Since we concentrate on environmental regulations and firm performance, we do not exploit

the data on environmental benefits from the after sales use of a good or service by the end user.

16

Table 1: Sample coverage (number of manufacturing firms)

PS CIS ECF

2002 5751 8782

2004 4966 2538 7867

2006 4300 2133 7296

2008 3808 2164 7230

PS= Production Statistics Survey; CIS=Community Innovation Survey; ECF=Survey on Environ-

mental Costs of Firms.

17

Table 1 summarizes the coverage of different surveys for manufacturing before data link-

ing and before deleting “item non-response” and/or implausible values (such as a recorded neg-

ative value added). The ECF survey has the highest coverage and the CIS survey the lowest. To

include as many observations as possible we chose not to start with the data that are available

after matching all three available surveys. Instead, we tried to maximize the number of obser-

vations by taking all the yearly data from the ECF and PS surveys and repeating the data from

CIS for two successive years. For the modeling of the three types of eco-investment we used

essentially the ECF and PS panel. The only variable that came from CIS was the environmental

regulation. For that variable we put the values for the years 2003, 2005 and 2007 equal to those

for 2004, 2006 and 2008 respectively, which is not unreasonable since the CIS surveys of 2004,

2006 and 2008 cover respectively the periods 2002-2004, 2004-2006, and 2006-2008. The pre-

dictions from the eco-innovation investment equations are then used for modeling the eco-in-

novation outputs. At this stage we absolutely need the CIS data because it is the only source

that collects data on the perception of environmental regulations. The dummy variables that are

taken from CIS, i.e. the two eco-innovation choices, environmental regulations and innovation

cooperation, are again imputed for the years 2003, 2005 and 2007 as explained above. All other

variables are directly taken from the yearly surveys.

Table 2 presents some descriptive statistics for the variables used in the models. The

means of the variables do not change very much before and after merging datasets. It can be

seen that about half as much is paid on eco-R&D as on the other two types of (non R&D) eco-

investments. The end-of-pipe eco-investment is roughly twice as big as the process-integrated

eco-investment. About 30 % of the firms responded to environmental regulations, either exist-

ing or anticipated. Approximately 30% of the firms in the sample underlying the productivity

18

equation had introduced resource-saving eco-innovations and 3% more had introduced pollu-

tion-reducing eco-innovations.10

10 Notice that we have constructed the predicted eco-investments per fte conditional on doing an eco-investment

also for observations for which some observations on environmental levies were missing. Therefore we have

slightly more observations for the eco-innovation output equations than for the eco-investment equations.

19

Table 2: Descriptive statistics

Eco- investment equations Eco-innovation equations Productivity equation

N Mean Std N Mean Std N Mean Std

Employment in fte *) 5989 132.6 292.3 6039 132.4 291.3 6581 143.1 293.8

Eco subsidies received (dummy) 5989 0.339 0.473 6039 0.340 0.474

Eco-R&D per fte (1000 Euro) in t 5987 0.106 0.256 6039 0.063** 0.043 6581 0.113 0.320

End-of-pipe eco-investment per fte (1000 Euro) in t 5987 0.137 1.487 6039 0.014** 0.019 6581 0.168 2.409

Process-integrated eco-investment per fte (1000 Euro) in t 5987 0.070 0.571 6039 0.020** 0.026 6581 0.085 0.980

Energy cost shares in total production costs *) 5989 0.017 0.024

Environmental levies/ total environmental exploitation costs *) 5989 0.081 0.121

Existing and anticipated environmental regulations (dummy) 5989 0.285 0.451 6039 0.284 0.451 6581 0.300 0.458

Pollution-reducing eco-innovations (y31, dummy) 6039 0.321 0.467 6581 0.334 0.472

Resource-saving eco-innovations (y32, dummy) 6039 0.287 0.453 6581 0.302 0.459

Innovation cooperation (dummy) 6039 0.268 0.443

Gross output per fte (1000 Euro) 6581 229.2 311.3

Capital inputs per fte (1000 Euro) 6581 7.4 10.0

Material inputs per fte (1000 Euro) 6581 167.3 294.0

Value added per fte (1000 Euro) 6581 61.8 39.3

*) In the eco-innovation investment models and the eco-innovation output model we used one-year lagged variables.

** Conditional predictions of eco-innovation investments per fte from tobit type II model for 2003-2008.

20

5. Discussion of the results

We shall now present and discuss the estimation of each part of the model: the invest-

ment equations, the innovation output decisions and the contribution of innovation to the

productivity performance. The focus of this paper is on the contribution of ER to innovation.

We postulate that environmental investment can be brought into the picture for obtaining a more

in-depth analysis of the Porter Hypothesis letting ER affect the different stages of innovation

and indirectly productivity.

We pool the data for the years 2003 to 2008. We control for industry effects and year

fixed effects (except for the investment selection equations). Some of the variables are lagged

by one year to partly circumvent an endogeneity problem.

a. Eco-investment

The selection and the outcome equations of the investment decisions were estimated sim-

ultaneously by maximum likelihood using the tobit type II model. The results for the probit part

of the estimates (see Table 3) clearly indicate that selectivity is present in the data: at least for

eco-R&D and end-of-pipe eco-investments the correlation coefficients between the error terms

in the selection and the outcome equations are statistically significant. Larger firms tend to

invest more in eco-R&D but less in the other two types of eco-investment. The intensity of eco-

investments decreases with size. The energy cost share, environmental levies and environmen-

tal regulation all push firms to invest in eco-R&D and other eco-investments. Firms tend to

invest more in eco-innovation when the relative price of investment decreases, when the energy

cost goes up, when they get innovation subsidies or when they are forced to innovate because

of environmental regulation. Almost all the firms do some eco-R&D and therefore they are less

21

responsive to ER for increasing their eco-R&D. The other two types of eco-investments react

more strongly to ER with semi-elasticites of 0.4 and 0.32.

Thus, already at the investment stage of innovation, there is a role for ER and market

based incentives in the form of taxes, price and cost considerations in explaining differences in

eco-investment intensities.

21

Table 3: Eco-investment equations (tobit type II)

eco-R&D end-of-pipe process integrated

Eco-investments

N total 5987 5987 5987 N censored 28 3666 3829

Selection coefficient SE coefficient SE coefficient SE

log(employment in fte) in t-1 0.25*** 0.07 -0.06*** 0.02 -0.06*** 0.02

log(energy cost share) in t-1+ 0.21*** 0.06 0.06*** 0.02 0.05*** 0.02

log(environmental levies share) in t-1 * 0.06 0.07 0.06*** 0.01 0.07*** 0.01

environmental regulation dummy 0.36* 0.21 0.18*** 0.04 0.20*** 0.04

constant 2.72*** 0.51 0.39*** 0.11 0.32*** 0.11

log(eco-investment per fte) coefficient SE coefficient SE coefficient SE

log(employment in fte) in -1 -0.14*** 0.02 -0.08* 0.04 0.03 0.05

environmental regulation dummy 0.10*** 0.03 0.40*** 0.09 0.32*** 0.09

log(p_investment/p_labor) in t-1 -0.49*** 0.06 -0.65*** 0.13 -0.34*** 0.12

log(energy cost share) in t-1 0.10*** 0.02 0.41*** 0.05 0.36*** 0.05

eco subsidies received dummy 0.81*** 0.05 1.04*** 0.11 1.25*** 0.14

industry dummies yes yes yes time dummies yes yes yes

rho 0.45*** 0.06 0.80*** 0.03 0.51 0.16

22

Log likelihood -8619.4 -8228.8 -7908.9

+ in total costs *in total environmental exploitation costs

23

b. Eco-innovation

The main focus of this paper is on the innovation decisions of firms (i.e. the innovation

output stage of our “Green CDM” model). Table 4 presents the results for the model that uses

two types of innovations: pollution-reducing and resource-saving innovations. The former can

be assimilated with end-of-pipe eco-innovations, the latter with process-integrated eco-innova-

tions. We report two types of estimates, those of a bivariate probit model in which the effects

of common unobservable variables are captured by correlations between the error terms of the

three equations, and a simultaneous bivariate probit model with endogenous dummies, our

model (3) inspired by Lewbel (2007), in which we allow for complementarity between the two

innovation adoption decisions. The former model is nested in the latter and is clearly preferred

to the latter by a likelihood ratio test. We shall therefore base the discussion on the estimates

from the model with simultaneity.

24

Table 4: Innovation outputs (bivariate probit model, with and without simultaneity)

Without simultaneity With simultaneity

Pollution-reducing

eco-innovations

Resource-saving

eco-innovations

Pollution-reducing

eco-innovations

Resource-saving

eco-innovations

ME a) SE ME a) SE ME a) SE ME a) SE

N observations (2002 – 2008) 6039 6039

log(fte) t-1 0.01 0.01 0.02 0.01 0.12*** 0.01 0.00 0.00

predicted log(eco-R&D per fte) -0.04 0.05 0.16*** 0.04 0.36*** 0.06 0.24*** 0.04

predicted log(end-of-pipe eco-investment per fte) 0.13** 0.05 0.06 0.05 0.12* 0.06 0.04 0.04

predicted log(process-integrated eco-investment per fte) -0.06 0.06 0.06 0.06 -0.37*** 0.07 0.10** 0.05

environmental regulation 0.57*** 0.02 0.42*** 0.01 0.37*** 0.02 0.22*** 0.01

innovation cooperation 0.15*** 0.01 0.13*** 0.01 0.50*** 0.02 0.24*** 0.01

industry dummies yes yes

year dummies yes yes

synergy between both types of innovation output - - 0.47*** 0.03

rho 0.68*** b) 0.02 0.01*** b)

Log likelihood -4591.41 -6898.96

a) The marginal effects are evaluated at the means of the covariates. b) The rho parameter is calculated using “generalized residuals” (see Gouriéroux et al., 1987).

25

Eco-R&D has a positive effect on both types of innovations. A one percent increase in

eco-R&D increases the probability of adopting a pollution-reducing innovation by 0.36 per-

centage points and the probability of adopting a resource-saving innovation by 0.24 percentage

points. End-of-pipe eco-investments have a weak effect on eco-innovation: a marginal effect of

0.12, significant only at 10%, for pollution-reducing innovations and an insignificant effect on

resource-saving innovations. A one percentage increase in process-integrated eco-investments

decrease by 0.27 percentage points the likelihood of obtaining a pollution-reducing innovation

but increase by 0.10 percentage point the probability of obtaining a process-integrated innova-

tion. These direct effects get magnified by the synergy between the two types of innovations as

the presence of one type of innovation increases by 47 percentage points the occurrence of the

other type of innovation. Consequently the total effects of any exogenous changes in the deter-

minants of innovation are roughly twice as large as the direct effects.

Our results also show that innovation cooperation increases the incidence of both types

of innovation but that size only “matters” for pollution-reducing innovation. Most interestingly,

our results show that environmental regulations influence the incidence of both types of inno-

vation. The presence of ER increases by 45 percentage points the occurrence of pollution-re-

ducing eco-innovation [0.45=exp(0.37)-1], and by 25 percentage point the occurrence of re-

source-saving innovation. In other words, in addition to the indirect effect of ER on innovation

investment, there is also an important direct effect of ER on the incidence of each type of eco-

innovation. We consider this last result as a strong corroboration of the weak version of the PH.

c. Productivity

This section looks at the productivity impact of different types of eco-innovations, i.e. it

examines indirectly the strong version of the PH. The OLS estimates presented in the first two

columns of table 5 show that there are hardly any economies or diseconomies of scale: the

26

coefficient of the logarithm of employment is not different from 0. The direct effect of eco-

innovation is negative for pollution-reducing innovations and non-significant for resource-sav-

ing innovations. Environmental regulation does not make a statistically significant difference.

However, a drawback of the OLS estimation is that the innovation dummies are not

exogenous. To circumvent these shortcomings we have re-estimated the productivity equation

using the GMM instrumental variables (IV) method. The GMM estimation presented in col-

umns 3 and 4 uses the predicted propensities derived from the innovation output model (3) as

instruments for the two eco-innovation outputs. In the last two columns of table 5 we also let

the traditional factors of production be endogenous and instrument them by their one-period

lagged values. The results of the GMM estimation clearly show that the endogeneity of the

innovation output dummies is an important issue. Although the coefficients have quite different

magnitudes, in essence they convey the same story. End-of-pipe eco-innovations are negatively

correlated to productivity whereas production-integrated eco-innovations are positively corre-

lated to TFP. Whenever we introduced environmental regulation directly in the productivity

equation, it never turned out significant. In practice both types of eco-innovation occur jointly:

the frequencies of occurrence of resp. end-of-pipe and process-integrated eco-innovations are

63% for (0,0), 6% for (0,1), 10% for (1,0) and 21% for (1,1). This high frequency of co-occur-

rence confirms the complementarity reported in the previous section. It also explains why the

environmental innovation is insignificant when not split into its two components: most of the

time the two innovations occur jointly, the chances of single occurrence are almost equal and

the marginal effects are also almost equal but of opposite sign.

Unlike most of the literature (see Ambec at al, 2011 and Lanoie et al., 2011), we do

come up with a corroboration of the Porter hypothesis but only for process-integrated eco-in-

27

novations. As Horbach and Rennings (2012) have found with German data regarding the em-

ployment effects of environmental innovations, only process-integrated eco-innovations have a

positive effect on economic performance.11

11 In a previous version of the paper we tried to examine the complementarity/substitutability between eco-inno-

vations and product or process innovations. Unfortunately we cannot separate the eco and non-eco product and

process innovations, and therefore product and process innovations partly contain eco-innovations. Contrary to

Marin (2012) who used a model similar to ours but patent counts instead of innovation occurrences as a measure

of innovation output on Italian data, we did not find that environmental innovations crowd out technological inno-

vations.

28

Table 5: Labor productivity (in log)

OLS GMM a) GMM b)

coeff. SE coeff. SE coeff. SE

log(capital/labor) 0.05*** 0.00 0.05*** 0.01 0.06*** 0.01

Log(intermediate inputs/labor) 0.76*** 0.00 0.77*** 0.01 0.77*** 0.01

log(labor) -0.00 0.00 -0.01 0.01 -0.01* 0.00

pollution-reducing eco-innovations -0.09** 0.04 -0.48*** 0.15 -0.52*** 0.17

resource-saving eco-innovations 0.00 0.00 0.51*** 0.17 0.56*** 0.19

_cons 1.48*** 0.01 1.47*** 0.03 1.47*** 0.03

Year dummies yes yes yes

Industry dummies yes yes yes

R2 0.96

N 6581 4606 4516

a) The two types of eco-innovations are instrumented by all exogenous variables and the predicted occurrence of the

eco- innovation adoption obtained from the estimates reported in table 4.

b) The two types of eco-innovations and the three inputs are instrumented by all exogenous variables, the lagged inputs

and the predicted occurrence of the eco-innovations obtained from the estimates reported in table 4.

Significant at 1% (***), 5% (**), 10% (*).

No Hansen test is reported since there is no overidentification.

29

Conclusion

This paper presents a new attempt to investigate the validity of the Porter hypothesis using

a more structural modeling approach than mostly used up to now in the mainstream of empirical

research on this topic. We apply a “Green type of CDM” innovation model to a very compre-

hensive data set built after matching three Dutch firm survey data. We distinguish three types

of eco-investments: eco-R&D, end-of-pipe eco-investments and process-integrated eco-invest-

ments and two types of eco-innovation outputs: pollution-reducing and resource-saving. We

model the determinants of eco-investments, eco-innovations and productivity, with eco-invest-

ments affecting innovation outputs and the latter affecting productivity. We are particularly

interested in testing the so-called Porter hypothesis that predicted a positive impact of environ-

mental regulations not only on eco-investments and eco-innovations but also on economic per-

formances like total factor productivity.

Our empirical results strongly corroborate the weak version of the PH. There is a signifi-

cantly positive contribution of existing or anticipated environmental regulations on eco-inno-

vations, directly and indirectly via their positive effect on eco-investments that in turn boost the

propensity of introducing environmental innovations. This driving effect is strengthened by the

complementarity between the two types of eco-innovations. Moreover the use of environmental

levies seem to be an important element in the decision making of firms to invest in eco-R&D

and eco-investments and play indirectly a major role in the introduction of eco-innovations.

Whereas many studies cannot corroborate the strong version of the PH we are able to

detect one way in which environmental regulations can boost total factor productivity. Re-

source-saving eco-innovations, which can be assimilated to process-integrated eco-innovations,

increase total factor productivity, whereas pollution-reducing, i.e. end-of-pipe, eco-innovations

tend to reduce TFP. The marginal effects of both are almost equal, and in the Netherlands at

least they occur mostly jointly and have about the same propensity of occurring individually.

30

Therefore eco-innovation globally does not turn out significantly. Environmental regulations

do not affect TFP directly. Eco-regulations, if properly aimed at process-integrated eco-inno-

vations, can have a positive effect on TFP. And maybe if we allowed for more time between

the inception of regulations, the occurrence of innovations and their effect on productivity, we

would get an even stronger result.

31

References

Acemoglu, Daron, Philippe Aghion, Leonardo Bursztyn and David Hemous, 2012, “The envi-

ronment and directed technical change”. American Economic Review, Vol. 102(1), pp. 131–

166.

Ambec, Stefan and Philippe Barla, 2002, “A theoretical foundation of the Porter

Hypothesis”. Economic Letters, Vol. 75, pp. 355–360.

Ambec, Stefan and Philippe Barla, 2006, “Can environmental regulation be good for Business?

An assessment of the Porter hypothesis”. Energy Studies Review, Vol. 14, Issue 2, Article 1.

Ambec, Stefan, Mark A. Cohen, Stewart Elgie and Paul Lanoie (2011), “The Porter

hypothesis at 20”, Discussion Paper 11-01, Resources for the Future.

Amemiya, Takeshi, 1984, “Tobit models: a survey”. Journal of Econometrics, Vol. 23, pp. 3–

62.

Cerin, Pontus, 2006, “Bringing economic opportunity into line with environmental influence:

A discussion on the Coase theorem and the Porter and van der Linde hypothesis”. Ecological

Economics, Vol. 56, pp. 209–225.

Chung, Y. H., R. Färe and S. Grosskopf, 1997, “Productivity and undesirable outputs: A direc-

tional distance function approach”. Journal of Environmental Management, Vol. 51, pp. 229–

240.

Cappellari, Lorenzo and Stephen P. Jenkins, 2003, “Multivariate Probit regression using sim-

ulated maximum likelihood”. The Stata Journal, Vol.3, No3, pp. 278–294.

Cappellari, Lorenzo and Stephen P. Jenkins, 2006, “Calculation of multivariate normal proba-

bilities by simulation, with applications to maximum simulated likelihood estimation”. The

Stata Journal, Vol.6, No 2, pp. 156–189.

32

Constantatos, Christos and Markus Hermann, 2011, “Market inertia and the introduction of

green products: Can strategic effects justify the Porter hypothesis?”. Environmental and Re-

source Economics, Vol. 50, pp. 267–284.

Crépon, Bruno, Emmanuel Duguet and Jacques Mairesse, 1998, “Research, innovation and

productivity: an econometric analysis at the firm level. Economics of Innovation and New

Technology, Vol. pp. 115–158.

Desrochers, Pierre, 2008, “Did the invisible hand need a regulatory glove to develop a green

thumb? Some historical perspective on market incentives, win-win innovations and the Porter

hypothesis”. Environmental and Resource Economics, Vol. 41, pp. 519–539.

Domazlicky, Bruce R. and William L. Weber, 2004, “Does environmental protection lead to

slower productivity growth in the chemical industry?” Environmental and Resource Econom-

ics, Vol. 28, pp. 301–324.

Gans, Joshua, S., 2012, “Innovation and climate change policy”. American Economic Journal,

Vol. 4(4), pp. 125–145.

Gourieroux, Christian, Alain Monfort, Eric Renault and Alain Trognon, 1987, “Generalized

residuals”. Journal of Econometrics, Vol. 34, pp. 5–32.

Heckman, James, J., 1978, “Endogenous variables in a simultaneous equation system”. Econo-

metrica, Vol. 46, No 4, pp. 931–959.

Horbach, Jens and Klaus Rennings, 2012, “Environmental innovation and employment dynam-

ics in different technology fields – An analysis based on the German Community Innovation

Survey 2009”. ZEW Discussion Paper No. 12-006. ZEW (Centre for European Economic Re-

search), Mannheim, Germany.

Jaffe, Adam, B., Richard G. Newell and Robert N. Stavins, 2002, “Environmental policy and

technological change”. Environmental and Resource Economics, Vol. 22, pp. 41–69.

33

Jaffe, Adam, B., Richard G. Newell and Robert N. Stavins, 2003, “Technological change and

the environment”. Chapter 11 in: Handbook of Environmental Economics, Vol. 1. Edited by

K. G Mäler and J. R. Vincent. Elsevier Science Publishers.

Jaffe, Adam and K. Palmer, 1997, “Environmental regulation and innovation: A panel data

study”, Review of Economics and Statistics, Vol. 79, No. 4, pp. 610-619.

Kemp R. (2011), Eco-Innovation: definition, measurement and open research issues,

Economia Politica, n. 1, in press.

Kodde, David, A. and Franz Palm, 1986, “Wald criteria for jointly testing equality and inequal-

ity restrictions”. Econometrica, Vol. 54, No. 5, pp. 1243–1248.

Kretschmer, Tobias, Eugenio J. Miravete and José C. Pernías (2012), “Competitive pressure

and the adoption of innovations”. American Economic Review, Vol 102, No. 4, pp.1540-1570.

Kriechel, Ben and Thomas Ziesemer, 2009, “The environmental Porter hypothesis: Theory ev-

idence and a model of timing of adoption”. Economics of Innovation and New Technology,

Vol. 18, No 3, pp. 41–69.

Lanoie, Paul, Jérémy Laurent-Luccheti, Nick Johnstone and Stefan Ambec, 2011, “Environ-

mental policy, innovation and performance: New insights on the Porter hypothesis”. Journal of

Economics and Management Strategy, Vol. 20, No. 3, pp. 803-842.

Lewbel, Arthur, 2007, “Coherency and completeness of structural models containing a dummy

endogenous variable”. International Economic Review, Vol. 48, No 4, pp. 1379–1392.

Marin, Giovanni, 2012, “Do eco-innovations harm productivity growth through crowding out?

Results on an extended CDM model for Italy”. IMT Lucca EIC working paper series 03.

McFadden, D. L., 1973. “Conditional logit analysis of qualitative choice behavior,” in Frontiers

in Econometrics (P. Zarembka, ed.). New York: Academic Press.

34

Milgrom, Paul and John Roberts, 1990, “The economics of modern manufacturing,

technology, strategy and organizations”. American Economic Review, Vol. 80,

pp. 511–528.

Milgrom, Paul and John Roberts, 1995, “Complementarities and fit. Strategy, structure and or-

ganizational change in manufacturing”. Journal of Accounting & Economics, Vol. 19, pp. 179–

208.

Miravete, E. and J. Pernías (2006). “Innovation complementarity and scale of production”.

Journal of Industrial Economics, Vol. 54, pp. 1-29.

Mohnen, Pierre and Lars-Hendrik Röller, 2005, “Complementarities in innovation policies”.

European Economic Review, Vol. 49, pp. 1431–1450.

Mohr, Robert D., 2002, “Technical change, external economies, and the Porter hypothesis”.

Journal of Environmental Economics and Management, Vol. 43, pp. 158–168.

Muller, Nicholas Z., Robert Mendelsohn and William Nordhaus, 2011, “Environmental ac-

counting for pollution in the United States economy”. American Economic Review, Vol. 101,

pp. 1649–1675.

Palmer Karen, Wallace E. Oates and Paul R. Portney, 1995, “Tightening environmental stand-

ards: The benefit-cost or no-cost paradigm?”. Journal of Economic Perspectives, Vol. 9 (4), pp.

119–132.

Polder, Michael, George van Leeuwen, Pierre Mohnen and Wladimir Raymond, 2010, “Prod-

uct- process and organizational innovation: drivers, complementarity and Productivity effects”.

UNU-MERIT Working Paper 2010-035, UNU-MERIT, Maastricht.

Popp, David, Richard G. Newell and Adam B. Jaffe, 2002, “Energy, the environment, and tech-

nological change”. Chapter 21 in: Handbooks in Economics, Vol. 2. Elsevier Science Publish-

ers.

35

Porter, Michael, E.,1991, “America’s green strategy”. Scientific American, Vol. 264, pp. 168.

Porter, Michael, E and Claas van der Linde, 1995, “Toward a new conception of the environ-

ment-competitiveness relationship”. The Journal of Economic Perspectives, Vol. 9, No 4, pp.

97-118.

Rennings, Klaus and Christian Rammer, 2010, “The Impact of Regulation-driven

environmental innovation on innovation success and firm performance”.

ZEW Discussion Paper No. 10-065. ZEW (Centre for European Economic Research), Mann-

heim, Germany.

Rennings, Klaus and Sascha Rexhäuser, 2010, “Long-term impacts of environmental policy

and eco-innovative activities of firms”. ZEW Discussion Paper No. 10-074. ZEW (Centre for

European Economic Research), Mannheim, Germany.

Rexhäuser, Sascha and Christian Rammer, 2014, “Environmental innovations and firm-profit-

ability: Unmasking the Porter hypothesis”. Journal of Environmental and resource Economics

57(1), 145-167.

Tamer, Elie, 2003, “Incomplete simultaneous discrete response model with multiple equilib-

ria”. The Review of Economic Studies. Vol. 70, No 1, pp. 147–165.

Train, Kenneth, 2003, Discrete Choice Methods with Simulations. Cambridge University Press,

Cambridge UK.

Wagner, Marcus, 2003, “The Porter hypothesis revisited: A literature review of

theoretical models and empirical tests”. Research Memorandum Center for Sustainability Man-

agement (SM) University of Lüneburg. Lüneburg, Germany.

Weiss, Jan F., 2015, Essays on externalities, regulation, institutions, and firm performance.

Jönköping International Business School, Jönköping University, Dissertation No, 102.

36

Wooldridge, J. M., 2002, Econometric Analysis of Cross Section and Panel Data.

MIT Press, Cambridge Massachusetts, Cambridge USA.

37

Annex: The likelihood function for the simultaneous multivariate probit model

In this appendix we describe the derivation of the likelihood function for our empirical

application. The computational complexities arise due to the requirement to have full error sup-

port over all possible combinations (strategy choices). Suppose there are N=3 types of innova-

tion. Then there are eight possible combinations of the three types of innovation. Thus, for every

adopted combination, seven comparisons are at stake [ ]. To keep things tractable we

will focus on strategy (0,0,0), i.e. no innovation at all (thus all comparisons are against zero

profits). This yields the following set of inequalities: 12

(B1)

231312

3322111)1,1,1()0,0,0( xxxVV

32141432 dUBUB

12 We use superscripts to denote the sum of ij and ji . Thus, .jiij

ij

)12( N

dUBUBxVV 33333)1,0,0()0,0,0(

dUBUBxVV 2121222)0,1,0()0,0,0(

322223

23

33222)1,1,0()0,0,0( dUBUBxxVV

dUBUBxVV 1111111)0,0,1()0,0,0(

212122

12

22111)0,1,1()0,0,0( dUBUBxxVV

313133

13

33111)1,0,1()0,0,0( dUBUBxxVV

38

In (B1) we make a distinction between the deterministic part (indicated by ) and the sto-

chastic part of the right-hand side (RHS). Notice that, for N = 3, we have one inequality involv-

ing two involving and four involving Any coherency problem is lifted if we take the

minimum of the upper bounds of the inequalities on the right-hand sides.

So we replace the inequalities for by and similarly for the inequal-

ities involving :

The (joint) probability for the case of no innovation at all is given by

X

X .

d

ijUB

,3 2 .1

2 ),min( 322212 dd UBUB

1

).,,,min( 3214313212111 dddd UBUBUBUB

}0,0,0Pr{ 321 yyy

),,,min(Pr{ 3214313212111 dddd UBUBUBUB

}&),min(& 33322212ddd UBUBUB

),,,min(Pr{ 3214313212111 dddd UBUBUBUB

}&),min(| 33322212ddd UBUBUB

}|),min(Pr{ 33322212ddd UBUBUB

}Pr{ 33dUB

39

Similar expressions can be derived for the other combinations of strategies. The expressions

involve conditioning upon unobservable variables to enable GHK simulation for evaluating the

integration bounds in the likelihood function. For example for P(0,0,0), the likelihood function

is given by

where f(.) stands for the density function of the normal distribution.

23

)3|322,

21min(

23

33 )|()(

dfdf

dUBdUBdUB

,),|( 132

)3,2|3214,313

,212,

11min(

1

df

dUBdUBdUBdUB