Biochemical Oxygen Demand (BOD)** **has been identified as an indicator of water pollution in the previous article. A level higher than 3mg/L is not suitable for drinking. In the case of river streams where wastewater flows, the limit is set to max 10 mg/L. Thus, the level higher than above-stated limits signifies water pollution. This causes a change in the chemical properties of the water and a** **reduction in the amount of dissolved oxygen in the water streams.

Low level of Biochemical Oxygen Demand is mainly due to an increase in solubility of water and algae productivity. On the other hand, higher-level is mainly due to sewage pollution, untreated domestic waste, the presence of nutrients like nitrate and phosphate. Presence of potassium worsens the level of Biochemical Oxygen Demand** **present in the water (Chattopadhyay et al, 1988; Naseema, Masihur, & Husain, 2013; Usharani et al, 2010).

This article establishes the impact of *Foreign Direct Investment (FDI)* inflows on the level of Biochemical Oxygen Demand in the Indian rivers through time series regression analysis. The methodology followed has been explained in the previous article.

## Presence of Biochemical Oxygen Demand in Indian rivers

Biochemical Oxygen Demand shows the amount of oxygen required by microorganisms to convert organic matter into an inorganic form. A higher amount of decomposable organic matter in water leads to the need for more oxygen and hence results in higher Biochemical Oxygen Demand. According to Basavaraddi, Kousar, & Puttaiah (2012), Hassan et al, (2017), Naseema et al. (2013), Pandey, Raghuvanshi, & Shukla (2014), there is a very high level of Biochemical Oxygen Demand in Indian river streams. The main reason behind this high level is the discharge of untreated domestic waste into the rivers, which tends to increase the organic matter in the water. For example- Yamuna has Biochemical Oxygen Demand range varying from 5.33 mg/L to 43.39 mg/L, and Ganga at Siddhnath Ghat had Biochemical Oxygen Demand averaging at 29.12 mg/l in the monsoon.

The below graph shows the average level of Biochemical Oxygen Demand in 15 major Indian rivers for the period 2002-2017. The figure shows that the level of Biochemical Oxygen Demand in Indian rivers is significantly higher than the drinking water limit and recently crossed the drainage limit. The level of Biochemical Oxygen Demand has increased from 9.29 mg/L to 12.93 mg/L. The lowest level of Biochemical Oxygen Demand was recorded in 2013 i.e. 5.87 mg/l. From 2005 to 2016, many fluctuations were seen but still, the level remains close to 10 mg/L.

## Hypothesis to test

This article considers Biochemical Oxygen Demand as an indicator of water pollution. The variability in the data-set was found to be high. According to Lütkepohl & Xu, (2009), the, natural log transformation of the variable can be used to stabilize the data-set. Thus, to derive the impact of net *FDI* inflows on Biochemical Oxygen Demand (BOD) the Hypothesis for the study framed is

H_{0}: There is no significant impact of FDI inflows on BOD H_{A}: There is a significant impact of FDI Inflows on BOD

## Stationarity test

A stationary time series is the one wherein the mean and variance of the variable remain constant over time. As stationarity is the necessary condition for building a model to forecast the relationship between variables, thus it is essential to perform stationarity test for determining the impact of *FDI* inflows on water pollution (Adhikari K. & R.K., 2013; Gujarati & Porter, 2009; Nason, 2018).

Augmented Dickey-Fuller (ADF) test results show whether the variables are stationary or not. Results of the test are given below.

Variable | Test-statistic | 5% Critical value | p-value |
---|---|---|---|

LnBOD | -4.833 | -3.000 | 0.0000 |

LnFDI | -1.511 | -3.000 | 0.5283 |

LnFDI with drift | -1.511 | -1.771 | 0.0774 |

LnFDI with trend | -1.259 | -3.600 | 0.8976 |

DiffLnFDI | -3.584 | -3.000 | 0.0061 |

Table 1: ADF results

In the case of Biochemical Oxygen Demand, ADF test shows that the variable is stationary. As the p-value is 0.0000 < 0.05 the significance level, the null hypothesis of having unit root is rejected. This result is also verified by absolute test statistic > absolute critical value. Hence, LnBOD is the stationary variable.

For *FDI*, the initial p-value is 0.5283 > 0.05 thus the null hypothesis of unit root is not rejected. Furthermore, the testing was done in case of drift and trend to test the stationarity in case of intercept and deterministic term presence (Gujarati & Porter, 2009) but, the p-value is high i.e. 0.0774 and 0.8976. Thus, to overcome non-stationarity, the first-order differentiation of the variable was done. The result shows that for drift the stationarity is derived as the p-value is 0.0061 < 0.05. Hence the first-order differentiated value of *FDI* inflows is the stationary variable. Further, a study by Kostakis, Sardianou, Lolos, & Eleni, (2016) too stated that based on the p-value or test statistic, the stationarity level of the variable is determined. As the absolute test statistic value at level was less than the absolute critical value and even p-value was high, thus first-order differentiation was processed. At first order differentiation, *FDI* inflows derived stationarity.

DifflnFDI series was generated to represent the value of LnFDI.

## Cointegration test

Cointegration test has been performed to avoid the testing of spurious relationship i.e. to determine whether the dataset is actually interlinked or not (Gujarati & Porter, 2009). As in order to derive the effective and reliable results, it is essential to know that whether any linkage between the variables do exist or not, thus cointegration is tested before deriving the significant and acceptable results from the regression.

Johansen cointegration test depicts the long-run relationship between the variables. Results are represented in the below table.

Max. Ranks | Trace Statistic | 5% Critical Value | Max Statistic | 5% Critical Value |
---|---|---|---|---|

0 | 16.8519 | 15.41 | 13.0330 | 14.07 |

1 | 3.8189 | 3.76 | 3.8189 | 3.76 |

Table 2: Johansen Cointegration Test Results

The above table shows that the trace-statistic value is greater than the critical value for 0 and 1 rank i.e. 16.8519 > 15.41 and 3.8189 > 3.76. Even, max statistic value is greater than the critical value i.e. 13.0330 > 14.07 and 3.8189 > 3.76. Thus, the null hypothesis stating that there is no cointegration between *FDI* inflows and Biochemical Oxygen Demand is rejected. Hence, there exists long-run and short-run cointegration between the variables for the period 2002-2017. This relationship for the *FDI* and environmental pollution is also derived in a study by Kumar & Chander, (2016).

Herein, as the trace statistic value is greater than the critical value, thus null hypothesis was rejected, and it could be deduced that there exists long-run integration between *FDI* and CO2 emission. When the value of one variable varies the others too vary.

## Normality test

In order to have effective analysis of the dataset of time series, it is essential to have a normally distributed data. A normally distributed dataset states that the variable is symmetrically distributed. As the presence of normality is the essential condition for stating the linear relationship between *FDI* and water pollution via regression, thus normality is tested (Casson & Farmer, 2014)

Shapiro-Wilk test determines the nature of the distribution of the variables. The below table represents the result of the test.

Variable | P-value |
---|---|

LnBOD | 0.77478 |

Difflnfdi | 0.50621 |

Table 3: Shapiro-Wilk Test results

The results presented in the above table shows that the p-value of both the variables is greater than the significance level i.e. 0.77478 and 0.50621 > 0.05. Thus, the null hypothesis of having a normal distribution of the dataset is not rejected.

Hence, LnBOD and Difflnfdi are normally distributed. Kostakis et al., (2016) in their study support this criterion of determining the normality. As in case of Singapore, the p-value was greater than the significance level of the study, thus the dataset of the variables is normally distributed, and the model is efficient enough to derive the significant and reliable results. Hence, the model formulated to study the impact of *FDI* inflows on water pollution in this study is significant and could be studied to derive the results.

## Regression

The stationary, cointegrated and normally distributed form of the model is used to study the impact of net *FDI* inflows on Biochemical Oxygen Demand. The model is represented below:

Wherein,

Variables | Nature of variable | Description |
---|---|---|

ln(BOD)t | Dependent | Stationary form of Natural Log-transformation for average biochemical oxygen demand of Indian rivers at the t-time period |

Diffln(FDI)t | Independent | Stationary form of Natural log-transformation for net FDI Inflows at the t-time period |

α0,α1 | Coefficients | Intercept, Slope Coefficient |

fst | Error Term | Residual |

t | Time |

Table 4: Variable description of the regression equation

The results of the final model are given below.

LnBOD | Coefficient | t-value | p-value | R^{2} value | Adjusted R^{2} value |
---|---|---|---|---|---|

Difflnfdi | -.0914063 | -0.63 | 0.540 | 0.0295 | -0.0451 |

Constant | 2.209769 | 39.39 | 0.000 |

Table 5: Regression results of Final Model

Though the above table shows the results of the impact of *FDI* on biochemical oxygen demand, before concluding the impact analysis results, it is essential to test the specification of the model by checking the interdependence and variability of the predicted values. These diagnostic tests would help in verifying all the conditions of the classical linear regression model (Casson & Farmer, 2014).

## Autocorrelation test to diagnose the error terms

Autocorrelation test state that there is a relationship between error terms. Presence of autocorrelation in a time series led to degrading the validity and precision of the hypothesis results as the data is collected for a single variable at different time. Thus, it is essential to have a non-autocorrelated model for efficient results (Huitema & Laraway, 2006).

Durbin Watson test was performed to study the interlinkage between the residuals. Results of the testing are given below.

D-statistic | D_{L} | D_{U} | 4-D_{U} | 4-D_{L} |
---|---|---|---|---|

2.191111 | 0.946 | 1.543 | 2.457 | 3.054 |

Table 6: Durbin Watson Result

The above table shows that the value of D-statistic is between DU and 4-DU i.e. 1.543<2.191111<2.457. Thus, there is no autocorrelation present in the residuals. Hence, residuals are uncorrelated with each other. Okumoko, Akarara, & Opuofoni, (2018) in their study stated that the Durbin Watson statistic value close to 2 is said to be free from the problem of autocorrelation. As the value of the final model is approximately 2, thus the model is understood to be free from the problem of autocorrelation.

## Heteroscedasticity test to diagnose variance

Heteroscedasticity is the condition of having a difference in the variance value for the predictions of regression. This sometimes interprets misspecification of the model and even not fulfil the assumption of the regression. Hence, in order to depict the reliable results, it is essential to test heteroscedasticity and use the homoscedastic model to interpret results (Casson & Farmer, 2014; Salkind, 2007).

Bartlett’s Periodogram based white noise heteroscedasticity test depicts the level of variation present in the residuals. The result of the test is given below.

Bartlett’s (B)- Statistic | P-value |
---|---|

0.5410 | 0.9316 |

Table 7: Heteroscedasticity Test results

The above results show that the p-value of the test is greater than the significance level i.e. 0.9316 > 0.05. Thus, the null hypothesis of having no heteroscedasticity in the analysis is not rejected. Hence, the model is homoscedastic. This result was also verified in the case of Singapore (Kostakis et al., 2016). They stated that as the p-value of the model is greater the significance level of the study thus the presence of high variability in the predicted value is completely absent and the model is homoscedastic in nature.

*FDI* inflows do not affect Biochemical Oxygen Demand levels in Indian rivers

The final model does not have the problem of autocorrelation and heteroscedasticity thus the testing could be done. The R2 value is 0.0295 thus showing that about 3% of the variation in Biochemical Oxygen Demand value is due to *FDI* inflows. However, this variation is very less as Faraway, (2014) mentioned that for social science-based studies, the R2 value of 0.6 is good. Furthermore, the p-value test shows that the value is 0.540 > 0.05 the significance level.

Thus, the null hypothesis of *FDI* inflows having no significant impact on Biochemical Oxygen Demand is not rejected. Seltman, (2018) stated that the p-value is the probability of selecting the given statistic when the stated hypothesis is true. Thus, the value less than the significance level of the study shows that there is statistical significance in studying the stated hypothesis.

Above graph shows that the values of ln(BOD) are scattered away from the fitted line. Thus though the line explaining relationship between FDI inflows and biochemical oxygen demand is slightly negatively sloped but not much impact could be seen. Hence, there was no significant impact of FDI inflows in influencing the level of Biochemical Oxygen Demand in Indian rivers selected for the study from 2002-2017.

Hassaballa, (2013) studied the relationship between *FDI* and environment degradation by considering air and water pollutants. Taking Biochemical Oxygen Demand as an indicator of water quality, Hassaballa analysis showed that there is no impact of *FDI* inflows on the level of pollution emitted. The study concluded that manufacturing industries production technique is mainly the source of pollution. However, the implementation of water treatment technologies tends to reduce the pollution level (Hassaballa, 2013; OSEC, 2010; Sahasranaman & Ganguly, 2018).

The analysis in this article shows that with an increase in *FDI* inflows, Biochemical Oxygen Demand level decreases. But this relationship is not significant. The trend of Biochemical Oxygen Demand depicts that initially the level is increasing but *FDI* inflows are not the factor that influences this level.

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