5. Results

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, therefore, excluded Loglength and Logmse in Model 2.

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 that we can treat Mindisch as an independent variable.

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

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


Table 2. Regression results of Model 1 with different estimators, N ¼ 59.

than the logit model as measured by pseudo R<sup>2</sup> , Aikaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) tests.

shows the fish habitat conditions at a downstream segment, a higher level of VIX should be associated with a higher probability of a cost according to the simple economic theory presented in Section 2. On the other hand, a negative sign indicates that there is no conflict in the achievement of biodiversity targets and energy production. However, the estimate is not significant and

Model 1 Model 2 Model 1 Model 2

Logelprod 0.176\*\*\* 0.000 0.152\*\*\* 0.001 0.175\*\*\* 0.000 0.154\*\*\* 0.000

VIX 0.553 0.646 0.572 0.486 Mindisch<sup>a</sup> 0.384\*\*\* 0.065 0.157 0.750 0.375\*\* 0.042 0.166 0.655

Table 4. Estimates of marginal effects of each of the explanatory variable at the mean value of all variables.

dy/dx p-value dy/dx p-value dy/dx p-value dy/dx p-value

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

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

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dy/dx is for discrete change of dummy variable from 0 to 1.

Generally, coefficients of binary outcome models are in log-units and cannot directly be interpreted as marginal effects. This is due to the fact that the logit or probit transformation of the outcome variable has a linear relationship with the predictor variables. However, it is possible to derive the

The probit and logit models give similar marginal effects of Logelprod for both Model 1 and Model 2 (Table 4). The probability of a loss in electricity production increases by 0.18 (Model 1) or 0.15 (Model 2). An increase inMindisch has the largest impact on the probability, an increase by one unit raises the probability by 0.38 (Model 1). On the other hand, an increase in the natural conditions in

The purpose of this study was to determine if restoration of biodiversity in dry channels at hydropower plants in Sweden can be costly for the plants and how the probability of a cost is affected by the size of the plant, site-specific factors in the dry channels, and ecological status in downstream regions of the river. The measure considered for restoration is the existence of a program for minimum releases of water from the reservoirs to the dry channel, and the cost is defined as a decrease in electricity production. The study rests on data from a survey of the largest hydropower plants in Sweden, which resulted in data for 76 plants with dry channels. According to the responses in the survey, 58% of the plants with a program for minimum water discharges report a cost. The reasons for not reporting such a loss can be that it is considered as negligible or that the respondent has insufficient information. We cannot distinguish between

we cannot make conclusions about the effects of VIX on the probability of a cost.

Variable Logit Probit

p < 0.1; <sup>a</sup>

Loglength 0.164\* 0.053 0.156\*\* 0.035 Logmsek 0.280\*\*\* 0.000 0.277\*\* 0.000

individual marginal effects or elasticities of covariates at their mean values (Table 4).

the dry channel reduces the risk by 0.16 and 0.26 for Loglength and Logmsek, respectively.

6. Discussion and conclusions

Notes: \*\*\*p < 0.01, \*\*p < 0.05, \*

The results for the two estimators are similar when replacing Loglength and Logmsec with VIX, see Table 3.

The statistical performance of Model 2 as measured by the significance of explanatory variables, overall model significance pseudo R<sup>2</sup> , AIC, and BIC was lower than for Model 1, which may be explained by the lower number of observations. A common result for Model 1 and Model 2 was the positive and significant effect of Logelprod. Although Mindisch has the expected negative sign in Model 2, it was not significant. The estimate of VIX has an unexpected negative sign. Since VIX


Table 3. Regression results of Model 2 with different estimators, N ¼ 20.


Notes: \*\*\*p < 0.01, \*\*p < 0.05, \* p < 0.1; <sup>a</sup> dy/dx is for discrete change of dummy variable from 0 to 1.

Table 4. Estimates of marginal effects of each of the explanatory variable at the mean value of all variables.

shows the fish habitat conditions at a downstream segment, a higher level of VIX should be associated with a higher probability of a cost according to the simple economic theory presented in Section 2. On the other hand, a negative sign indicates that there is no conflict in the achievement of biodiversity targets and energy production. However, the estimate is not significant and we cannot make conclusions about the effects of VIX on the probability of a cost.

Generally, coefficients of binary outcome models are in log-units and cannot directly be interpreted as marginal effects. This is due to the fact that the logit or probit transformation of the outcome variable has a linear relationship with the predictor variables. However, it is possible to derive the individual marginal effects or elasticities of covariates at their mean values (Table 4).

The probit and logit models give similar marginal effects of Logelprod for both Model 1 and Model 2 (Table 4). The probability of a loss in electricity production increases by 0.18 (Model 1) or 0.15 (Model 2). An increase inMindisch has the largest impact on the probability, an increase by one unit raises the probability by 0.38 (Model 1). On the other hand, an increase in the natural conditions in the dry channel reduces the risk by 0.16 and 0.26 for Loglength and Logmsek, respectively.
