2. Theoretical framework

The theoretical framework rests on the assumption that each power plant minimizes costs for restoring biodiversity. This is a common assumption in economics where firms are assumed to use inputs, such as labor and capital, at given prices to minimize costs for producing certain outputs. By applying the so-called duality theory a cost function can be derived which shows the relation between the output and production cost (e.g., [9]). The cost is then expressed as a function of given input prices, and output level. In our case, biodiversity improvement constitutes the output Q<sup>i</sup> where i ¼ 1,.., n sites of the hydropower plants. The level of the output, or success of restoration, which can be measured as number of fish species or as a quality index, depends on ecological conditions at the site, Eil where <sup>l</sup> <sup>¼</sup> 1,.., <sup>m</sup> conditions such as length of the channel and natural water flow, and on restoration measures at the plant, Mig where <sup>g</sup> <sup>¼</sup> 1,.., h different restoration measures such as water discharges from the dam. The biodiversity at the site is then written as Q<sup>i</sup> <sup>¼</sup> <sup>Q</sup><sup>i</sup> (Mi<sup>1</sup> ,..,Mih; Ei<sup>1</sup> ,.., Eim).

A crucial assumption in our analysis is that the plant manager minimizes total cost for achieving a minimum level of biodiversity, Q\*<sup>i</sup> . Each restoration measure is then associated with a cost, Cig(Mig), and a maximum capacity of implementation, Mig. For example, there is a maximum limit of water discharges into the channel. Plant size, Ki , may also affect costs; a large plant can have more expertise for implementing restoration measures than a small plant. On the other hand, a larger plant may give rise to more damages in the downstream waters, the mitigation of which requires costly restoration measures. The decision problem for the plant manager is then written as:

$$\begin{aligned} \text{MinC}^i &= \sum\_{\mathcal{S}} \mathcal{C}^{\circ}(M^{\circ}; K^i) \\\\ \text{Subject to } & \mathcal{Q}^i(M^{\text{il}}, \dots, M^{\text{il}}; E^{\text{il}}, \dots, E^{\text{int}}) \succeq \mathcal{Q}^{\*i} \text{ and } \; M^{\circ} \le \overline{M}^{\circ} \end{aligned} \tag{1}$$

By applying the so-called duality theory to Eq. (1) we can express the cost of restoration at the plant as a function of the chosen restoration target Q\*<sup>i</sup> , ecological conditions at the site, Eig, and the restoration measures, Mig, which is written as follows:

$$\mathbf{C}^{i} = \mathbf{C}^{i}(\mathbf{Q}\*^{i}, \mathbf{E}^{i1}, ..., \mathbf{E}^{im}, \overline{\mathbf{M}}^{1}, ..., \overline{\mathbf{M}}^{ih}, \mathbf{K}^{i}) \tag{2}$$

Our main interest is to investigate the impact on costs of a marginal increase in the restoration ambition, Q\*<sup>i</sup> . The hypothesis is that the cost, Ci , increases since more of the restoration measures need to be implemented. In this case, there is a conflict between biodiversity restoration and electricity provision since resources that could be used for electricity production are used for biodiversity restoration. On the other hand, a non-positive effect would imply the opposite interpretation. As shown in Eqs. (1) and (2), a test of this hypothesis requires data, not only on Ci and Q\*<sup>i</sup> , but also on Eil , Mig, and Ki .

#### 3. Description of data

provision of renewable electricity production and accounts for approximately 47% of the total electricity production in the country [1]. Nuclear power is the second largest source of electricity and accounts for 34% of total energy production. Not only is hydropower a large source of electricity, but also acts a powerful regulatory device for the large fluctuations in demand and supply of electricity. Further, it is among the least expensive sources of energy as measured in

Establishments of hydropower plants change the hydrological conditions in the riverine landscape which affects habitats for animals and plants. Streams can be totally or partially dried and thereby destroying the habitats for several species and migration pathways for fish species. Although there is no national evidence on the extinction of species because of the hydropower production, the effects imply a degradation of habitats for red listed species [3],

In order to mitigate these effects water power plants may be run with a release of water from the reservoir(s) into the downstream dry channel (the old natural river channel). However, this may only be achieved at a cost in terms of less electricity production and hence fulfillment of the target on renewable energy. This study investigates whether such a cost exists, and which factors contribute to the probability of its occurrence. To this end, we use the costminimization framework to derive testable hypotheses. Test are made with data from a survey on 76 hydropower plants in Sweden with questions on the existence of a cost in terms of negative impact on electricity production, the type of water release from reservoirs, and characteristics of the dried downstream channel and the plant. This data set was completed with official statistics on ecological status in the downstream segments. We use econometric methods to examine the impact of water discharges from the reservoir and other explanatory variables on electricity production. The dependent variable is a binary variable which equals 1 when electricity production is affected and 0 otherwise. We, therefore, use a probit model for the regression analysis, where we estimate how the explanatory variables affect the

There is a large body of literature on ecological effects of biodiversity restoration in freshwaters, such as wetland restoration (see reviews in Refs. [4, 5]). Despite this, the literature on the determination of costs of measures mitigating biodiversity degradation from hydropower plants is scant (e.g., [6–8]). The cost of restoration objects depends on the investment and management of the restoration measure as such, and on the ecological conditions at the site affecting the need and quality of restoration [5]. In our view, the main contribution of this study is the estimation of the explanatory power of ecological conditions and water release from reservoirs on the probability of a restoration cost in terms of reduction in electricity

The theoretical framework rests on the assumption that each power plant minimizes costs for restoring biodiversity. This is a common assumption in economics where firms are assumed to

which goes against the national target of preserving biodiversity.

probability of losing electricity production.

SEK/kWh [2].

120 Selected Studies in Biodiversity

production.

2. Theoretical framework

Unfortunately, the necessary data presented in Section 2 is not available for a sufficient number of plants. Therefore, a survey was distributed to hydropower plants with dried channels. It turned out that the plant managers were not able to answer questions on our output variable, diversity at downstream sections of the reservoirs. The survey was therefore completed with official data on fish species.

The questionnaire was sent to the four largest hydropower companies in Sweden with any kind of restoration measures, where downstream dry or nearly dry river and stream channels had been identified and where electrofishing data were available for the dry or nearly dry channel downstream of the reservoir. The questionnaire was filled out and returned for 76 hydropower plants where fish data (see below) from downstream sections of the reservoirs were available. These plants are located in the entire Sweden, see Figure A1.

The survey included questions on the variables presented in Section 2: costs, measures for the release of water into the channel, ecological conditions of the dry river beds, and annual electricity production. The latter was used as a description of the characteristic of the plant. However, the respondents were not able to assess the costs of the measures, but on whether there had been a cost in terms of loss in electricity production. Therefore, our cost variable is binary, where Cost ¼ 1 when there is a loss in electricity production and Cost ¼ 0 otherwise.

natural downstream channel as a biodiversity restoration measure. It might be argued that mainly those dams with discharges of water from the reservoirs to the dry channel face a cost. However, the plants reporting a loss in electricity production is evenly distributed between

Variable Observations Mean Standard deviation Minimum Maximum

Elprod, electricity production in kWh 66 90,400,000 202,000,000 900 1,120,000,000 Length in m 75 2113 2612 62 16,308

/s 67 48 83 0 377

Biodiversity Restoration and Renewable Energy from Hydropower: Conflict or Synergy?

http://dx.doi.org/10.5772/intechopen.69134

123

Cost 66 0.576 0.498 0 1

Mindisch 75 0.47 0.50 0 1 Othmeas 75 0.69 0.46 0 1 VIX 20 0.43 0.23 0 1

The range in dam size as measured by electricity production is large within the dataset, ranging from 900 to 1,120,000,000 kWh/year (Table 1). The continuous variables Elprod, Length, and Msec are highly skewed, and we, therefore, transformed them into the logarithms Logelprod, Loglength,

We have employed the standard logit and probit models to estimate the explanatory power of the independent variables listed in Table 1 on the probability of a cost. The difference between the logit and probit model is the distributions of the error terms. The former follows a cumulative standard logistic distribution, whereas the later follows a cumulative standard normal distribution (see e.g., [13, 14]). The probability functions in both the models are symmetric around zero and tend to give similar parameter estimate. Therefore, we have estimated parameters of interest applying both estimators. We know that our dependent variable Cost, can take only two values, i.e., 1 if there is a cost and 0 if there is no cost. The probability of Cost ¼ 1 is p and the probability

Considering the probability that Cost ¼ 1 is a function of different covariates presented in Table 1, denoted by vector X, and parameters of interest β, we can write the standard binary

Consequently, the logit and probit models corresponding to Eq. (4) are given by Eqs. (5) and

E Cost ½ �¼ 1 � p þ 0 � ð1 � pÞ ) p ð3Þ

PðCost ¼ 1jXÞ ¼ fðβXÞ ð4Þ

of Cost ¼ 0 is (1�p). Hence, the expectation of Cost, E[Cost], is given as follows:

plants with and without minimum discharges to the dried channels.

and Logmsec.

Msec, water flow in m3

Table 1. Descriptive statistics.

4. Econometric model

choice model as follows:

(6), respectively, as:

With respect to the choice of measures, a common strategy is to implement a program with minimum water discharge from the reservoir to the old river bed, which ensures that there is a minimum flow of water in order to potentially sustain downstream stream and river organisms. A question was included on the existence of such a program (Mindisch) (by court order or voluntarily) where Mindisch ¼ 1 when the measure is in place and Mindisch ¼ 0 otherwise. The plants can also implement other strategies for improving biodiversity, such as an even flow of water to downstream water. A question was therefore included on the existence of other measures (Othmeas) where Othmeas ¼ 1 if such measures exist and Othmeas ¼ 0 otherwise.

Sufficient length of dry channels and natural water flow in the dry channels provide favorable ecological conditions for restoring biodiversity. Questions were included on the length of the dry channels (Length), and natural water flows in the dry channels in m/s (Msec) as continuous variables. The size of the plant was measured as the annual electricity production (Elprod).

As shown in Section 2, the variable measuring biological conditions of the downstream dry or partly dry stream or river section should reflect the effects of restoration measures and ecological conditions in the channel. This would require data and analysis of biological conditions before and after the implementation of the measures. Such data is not available. Instead, we use data on measurements of biological conditions in the downstream river section, which is available as electrofishing data at the Swedish Electrofishing Register [10]. The Swedish stream and river fish index VIX was used to assess the ecological status of the downstream sections [11]. The VIX index ranges from 0 to 1, where high values denote high ecological status and low values denote bad ecological status according to the EU Water Framework Directive [12].

Descriptive statistics of the dependent variable Cost and the independent variables are displayed in Table 1.

The results from the survey showed that 58% of all plants report a cost in terms of a reduction in electricity production and 47% have implemented minimum flow discharges into the old


Table 1. Descriptive statistics.

turned out that the plant managers were not able to answer questions on our output variable, diversity at downstream sections of the reservoirs. The survey was therefore completed with

The questionnaire was sent to the four largest hydropower companies in Sweden with any kind of restoration measures, where downstream dry or nearly dry river and stream channels had been identified and where electrofishing data were available for the dry or nearly dry channel downstream of the reservoir. The questionnaire was filled out and returned for 76 hydropower plants where fish data (see below) from downstream sections of the reservoirs

The survey included questions on the variables presented in Section 2: costs, measures for the release of water into the channel, ecological conditions of the dry river beds, and annual electricity production. The latter was used as a description of the characteristic of the plant. However, the respondents were not able to assess the costs of the measures, but on whether there had been a cost in terms of loss in electricity production. Therefore, our cost variable is binary, where Cost ¼ 1 when there is a loss in electricity production and Cost ¼ 0 otherwise. With respect to the choice of measures, a common strategy is to implement a program with minimum water discharge from the reservoir to the old river bed, which ensures that there is a minimum flow of water in order to potentially sustain downstream stream and river organisms. A question was included on the existence of such a program (Mindisch) (by court order or voluntarily) where Mindisch ¼ 1 when the measure is in place and Mindisch ¼ 0 otherwise. The plants can also implement other strategies for improving biodiversity, such as an even flow of water to downstream water. A question was therefore included on the existence of other measures (Othmeas) where Othmeas ¼ 1 if such measures exist and Othmeas ¼ 0 otherwise.

Sufficient length of dry channels and natural water flow in the dry channels provide favorable ecological conditions for restoring biodiversity. Questions were included on the length of the dry channels (Length), and natural water flows in the dry channels in m/s (Msec) as continuous variables. The size of the plant was measured as the annual electricity production (Elprod).

As shown in Section 2, the variable measuring biological conditions of the downstream dry or partly dry stream or river section should reflect the effects of restoration measures and ecological conditions in the channel. This would require data and analysis of biological conditions before and after the implementation of the measures. Such data is not available. Instead, we use data on measurements of biological conditions in the downstream river section, which is available as electrofishing data at the Swedish Electrofishing Register [10]. The Swedish stream and river fish index VIX was used to assess the ecological status of the downstream sections [11]. The VIX index ranges from 0 to 1, where high values denote high ecological status and low values denote bad ecological status according to the EU Water Framework Directive [12].

Descriptive statistics of the dependent variable Cost and the independent variables are displayed

The results from the survey showed that 58% of all plants report a cost in terms of a reduction in electricity production and 47% have implemented minimum flow discharges into the old

were available. These plants are located in the entire Sweden, see Figure A1.

official data on fish species.

122 Selected Studies in Biodiversity

in Table 1.

natural downstream channel as a biodiversity restoration measure. It might be argued that mainly those dams with discharges of water from the reservoirs to the dry channel face a cost. However, the plants reporting a loss in electricity production is evenly distributed between plants with and without minimum discharges to the dried channels.

The range in dam size as measured by electricity production is large within the dataset, ranging from 900 to 1,120,000,000 kWh/year (Table 1). The continuous variables Elprod, Length, and Msec are highly skewed, and we, therefore, transformed them into the logarithms Logelprod, Loglength, and Logmsec.

#### 4. Econometric model

We have employed the standard logit and probit models to estimate the explanatory power of the independent variables listed in Table 1 on the probability of a cost. The difference between the logit and probit model is the distributions of the error terms. The former follows a cumulative standard logistic distribution, whereas the later follows a cumulative standard normal distribution (see e.g., [13, 14]). The probability functions in both the models are symmetric around zero and tend to give similar parameter estimate. Therefore, we have estimated parameters of interest applying both estimators. We know that our dependent variable Cost, can take only two values, i.e., 1 if there is a cost and 0 if there is no cost. The probability of Cost ¼ 1 is p and the probability of Cost ¼ 0 is (1�p). Hence, the expectation of Cost, E[Cost], is given as follows:

$$E[\text{Cost}] = 1 \ast p + 0 \ast (1 - p) \Rightarrow p \tag{3}$$

Considering the probability that Cost ¼ 1 is a function of different covariates presented in Table 1, denoted by vector X, and parameters of interest β, we can write the standard binary choice model as follows:

$$P(\text{Cost} = \mathbf{1} | X) = f(\beta \mathbf{X}) \tag{4}$$

Consequently, the logit and probit models corresponding to Eq. (4) are given by Eqs. (5) and (6), respectively, as:

$$f\left(\boldsymbol{\beta}^{\prime}\boldsymbol{X}\right) = \frac{\boldsymbol{\sigma}^{\boldsymbol{\delta}^{\prime}\boldsymbol{X}}}{1 + \boldsymbol{\sigma}^{\boldsymbol{\delta}^{\prime}\boldsymbol{X}}}\tag{5}$$

The estimates give information on the probability of a cost from introducing restoration measures Mindisch and Othmeas, and the impacts of Logelprod, Loglength, and Logmsec. The

Biodiversity Restoration and Renewable Energy from Hydropower: Conflict or Synergy?

http://dx.doi.org/10.5772/intechopen.69134

Cost ¼ β<sup>6</sup> þ β7Logelprod þ β8Loglength þ β9Logmsec þ β10Mindisch þ β11Othmeas þ β12VIX þ ε

The results showed that the independent variable Othmeas was never significant, and we therefore excluded this variable. Another result was that the inclusion of all explanatory variables in Model 2 gave poor statistical fit because of the low number of observations. We,

There might also be statistical problems associated with endogeneity in the included explanatory variables. Since the purpose of minimum discharge (Mindisch) is to sustain ecological conditions in the dry channels, this variable might be dependent on the ecological status in the stream channels, Loglength, and Logmsec in Model 1 and VIX in Model 2. If so, the ordinary least square (OLS) estimates will not give consistent estimates (e.g., [15]). Therefore, we tested for endogeneity in Mindisch by using Loglength and Logmsec as instruments in Model 1 and VIX as an instrument in Model 2. Wald tests of both models showed that exogeneity in Mindisch could not be rejected at the 10% level (see, e.g., [15] for a description of the test). This means

We also tested for the existence of heteroscedasticity, which was not present in any model according to the results from Breach-Pagan tests (e.g., [16]). However, Pearson test of correlation among all explanatory variables showed significant associations at the 1% level between Logelprod and several other explanatory variables (Table A1). Despite these association, variance inflation factor (VIF) tests did not reveal problems of multicollinearity (mean VIF ¼ 1.29

The binary dependent variable denotes the likelihood of a cost of changes in any of the explanatory variables. We would expect Mindisch to increase the probability of a cost since this measure discharges water into the dry channel which could be used for electricity production. On the other hand, natural conditions in the dry channels, measured as channel length and natural water discharge, are likely to reduce the likelihood of a cost because there is less need for mitigation measures. As a measure of the size of the dam, Logelprod can increase the probability of a loss in electricity production. The regression results of Model 1 are presented in Table 2.

According to Table 2, the results from the logit and probit models are quite similar. All explanatory variables are significant and have the expected sign. The models are significant at the 0.01 level according to the model Chi-square statistic, and the predicted "Cost ¼ 1" corresponds to 87% of the observed "Cost ¼ 1." The statistical performance of the probit model is slightly better

ð11Þ

125

regression equation with VIX includes all variables and is specified as:

therefore, excluded Loglength and Logmse in Model 2.

that we can treat Mindisch as an independent variable.

for Model 1 and mean VIF ¼ 1.36 for Model 2).

Model 2:

5. Results

$$f\left(\boldsymbol{\beta}^{\prime}\boldsymbol{X}\right) = \boldsymbol{\Pi}\left(\boldsymbol{\beta}^{\prime}\boldsymbol{X}\right) = \int\_{-\infty}^{\boldsymbol{\beta}^{\prime}\boldsymbol{X}} \frac{1}{\sqrt{2\pi}} e^{-\frac{\mathbf{r}^{2}}{2}} du\tag{6}$$

Since probit and logit models are nonlinear in both parameter and variables, the usual ordinary least square (OLS) and weighted least square (WLS) estimators could not be plausible. For that reason, identification of parameters given by a vector β preferably should be obtained by applying the maximum likelihood (MLE) estimator. Generally, binary choice models can be derived from the latent variable model as it provides a link with standard linear regression models which makes interpretation of the parameters straightforward. Besides, the model illustrates the difference between logit and probit models. Suppose the binary outcome variable Cost and the corresponding latent variable Cost\* satisfies the single infix model as:

$$\mathbf{Cost}\* = \beta \mathbf{X} + \varepsilon \tag{7}$$

Given that Cost is observable, it can be expressed as:

$$\text{Cost} = \begin{cases} 1 & \text{if } \quad \text{Cost} \ast > 0 \\\\ 0 & \text{if } \quad \text{Cost} \ast \le 0 \end{cases} \tag{8}$$

Combining Eqs. (7) and (8), we can have the following response probabilities:

$$P(\text{Cost} = 1) = P(\beta X + \varepsilon > 0) = P(-\varepsilon < \beta X) = f(\beta X) \tag{9}$$

where, f β 0 X � � is the cumulative density functions (CDF). In the case of probit model, the error term follows the standard normal distribution whereas it follows the logistic distribution in the case of a logit model.

The signs of parameters β are directly interpretable in both logit and probit models, but not the magnitudes. For that reason, deriving the marginal effects and discrete changes in the estimates is crucial in order to obtain the magnitudes of parameters. The marginal effect of the continuous covariate is given by partial derivative with respect to that variable, whereas the discrete changes of dummy covariate are given by the difference in predicted probabilities of the variable at 0 and 1, setting other covariates constant at their reference points. Mathematical notion of marginal effects and discrete changes in binary outcome models can be found in Ref. [13].

Recall from Section 3 that the availability of data is limited for the VIX variable with only 20 observations. We, therefore, estimated regression equations with and without this variable. The regression equation without VIX is specified as:

Model 1:

$$\text{Cost} = \beta\_o + \beta\_1 \text{Logelprod} + \beta\_2 \text{Loglength} + \beta\_3 \text{Logmsec} + \beta\_4 \text{Mindisch} + \beta\_5 \text{Othmeas} + \varepsilon \quad (10)$$

The estimates give information on the probability of a cost from introducing restoration measures Mindisch and Othmeas, and the impacts of Logelprod, Loglength, and Logmsec. The regression equation with VIX includes all variables and is specified as:

Model 2:

f β 0 X � �

<sup>¼</sup> Π β<sup>0</sup> X � �

f β 0 X � �

Given that Cost is observable, it can be expressed as:

The regression equation without VIX is specified as:

where, f β

Model 1:

0 X � �

124 Selected Studies in Biodiversity

case of a logit model.

<sup>¼</sup> <sup>e</sup><sup>β</sup> 0 X

> ¼ ðβ 0 X

Since probit and logit models are nonlinear in both parameter and variables, the usual ordinary least square (OLS) and weighted least square (WLS) estimators could not be plausible. For that reason, identification of parameters given by a vector β preferably should be obtained by applying the maximum likelihood (MLE) estimator. Generally, binary choice models can be derived from the latent variable model as it provides a link with standard linear regression models which makes interpretation of the parameters straightforward. Besides, the model illustrates the difference between logit and probit models. Suppose the binary outcome vari-

able Cost and the corresponding latent variable Cost\* satisfies the single infix model as:

8 < :

Cost ¼

Combining Eqs. (7) and (8), we can have the following response probabilities:

1 þ e<sup>β</sup> 0

�∞

1 if Cost� > 0

0 if Cost � ≤ 0

PðCost ¼ 1Þ ¼ PðβX þ ε > 0Þ ¼ Pð�ε < βXÞ ¼ fðβXÞ ð9Þ

is the cumulative density functions (CDF). In the case of probit model, the error

term follows the standard normal distribution whereas it follows the logistic distribution in the

The signs of parameters β are directly interpretable in both logit and probit models, but not the magnitudes. For that reason, deriving the marginal effects and discrete changes in the estimates is crucial in order to obtain the magnitudes of parameters. The marginal effect of the continuous covariate is given by partial derivative with respect to that variable, whereas the discrete changes of dummy covariate are given by the difference in predicted probabilities of the variable at 0 and 1, setting other covariates constant at their reference points. Mathematical notion of marginal effects and discrete changes in binary outcome models can be found in Ref. [13].

Recall from Section 3 that the availability of data is limited for the VIX variable with only 20 observations. We, therefore, estimated regression equations with and without this variable.

Cost ¼ β<sup>o</sup> þβ1Logelprodþβ2Loglength þβ3Logmsec þβ4Mindisch þ β5Othmeas þε ð10Þ

1 ffiffiffiffiffiffi <sup>2</sup><sup>π</sup> <sup>p</sup> <sup>e</sup> �u2

<sup>X</sup> <sup>ð</sup>5<sup>Þ</sup>

Cost� ¼ βX þ ε ð7Þ

<sup>2</sup> du ð6Þ

ð8Þ

$$\begin{aligned} \text{Cost} &= \beta\_6 + \beta\_7 \text{Logelprod} + \beta\_8 \text{Logelength} + \beta\_9 \text{Logresc} \\ &+ \beta\_{10} \text{Mindisch} + \beta\_{11} \text{Othmeas} + \beta\_{12} \text{VIX} + \varepsilon \end{aligned} \tag{11}$$
