Electrical conductivity is an important indicator of water pollution. It represents the water’s ability to have electric current i.e. the amount of ionic content present in the water. As electrical conductivity represents the potability of water, thus it helps in indicating the fitness of water for consumption by humans and animals. A level of 1000 μmhos/cm is suitable for surface area and 2500 μmhos/cm for drinking purposes. Presence of conductivity higher than the above-stated level categories pollutes the water.

Mainly conductivity represents the number of dissolved solids. Thus, the discharge of wastewater consisting of organic toxins, metals, oils, and solids, and geology of the area are the main factors that tend to increase the amount of conductivity in streams and rivers (Bhateria & Jain, 2016; CPCB, 2008; Fri, 1972).

Studies by Bhateria & Jain (2016), reveal that in India, the presence of natural solids like granite and clay in the areas where streams or rivers flow influences the level of conductivity. However, apart from this, there are various human-based factors like sewage containing nitrate, chloride, and phosphate, tends to affect the conductivity of water.

Yamuna river’s conductivity went from 1097±117.30 to 1969±31.34 µScm−1(μmhos/cm). Agra city streams had conductivity level 740-9760 µScm−1 (μmhos/cm) pre-monsoon and 702-9250 µScm−1 (μmhos/cm).

CPCB, 2008; Hassan, Parveen, Bhat, & Ahmad, 2017)

The below figure shows that on average, Indian rivers’ water quality is very bad. The level of conductivity was very high for major Indian rivers from 2002-2017. Initially, the level was decreasing and reached 2355 μmhos/cm in 2006 but after that, the level increased. The conductivity amount in 2017 is much higher than the 2002 level.

There are various factors that are responsible for this rise in conductivity and **Foreign Direct Investment** **(FDI)** is one of them. The aim of this article is to study the impact of **FDI** inflows on the amount of electrical conductivity in the selected Indian rivers. For this purpose, data from 15 major Indian rivers were collected from 2007-2017. The data on water pollution indicators were obtained from the National Water Mission and Ministry of Statistics and Programme Implementation.

## Empirical analysis

In this article, the electrical conductivity level in the water is considered as an indicator of water pollution. The first step in a time series analysis is to check the data for variability. According to Lütkepohl & Xu, (2009), any dataset should be stable with minimum variation. The variability in this dataset was found to be high. Therefore using natural log transformation in MS Excel, the dataset was first stabilized. This stabilized dataset was then used for further analysis.

In order to test the impact of **FDI** inflows on the level of conductivity in the Indian rivers, the following hypothesis was framed.

H

_{0}: There is no significant impact of FDI inflows on electrical conductivity level in Indian riversH

_{A}: There is a significant impact of FDI inflows on electrical conductivity level in Indian rivers

## Precondition tests

The dataset should first be tested for stationarity, normality, and cointegration of the variables. Augmented Dickey-Fuller (ADF) test, Johansen cointegration test, and Shapiro-Wilk tests were applied respectively with the help of STATA.

### Stationarity

Stationarity is the property of the time series which ensures that the mean and variance value of the variable is constant. This assumption helps in determining the relationship reliably and forecasting (Adhikari, 2013; Gujarati & Porter, 2009; Nason, 2018). The below table represents the results of the ADF test for stationarity.

Variable | Test-Statistic | 5% Critical Value | p-value |
---|---|---|---|

LnConductivity | -2.491 | -3.000 | 0.1177 |

LnConductivity with drift | -2.491 | -1.771 | 0.0135 |

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 |

DiffFDI | -3.584 | -3.000 | 0.0061 |

Table 1: ADF results

In the case of conductivity, the absolute value of test-statistic is less than the absolute critical value i.e. 2.491<3.000. Even, the p-value is greater than the significance level of the study i.e. 0.1177>0.05. Thus, the null hypothesis of unit root without intercept is not rejected.

Furthermore, for LnConductivity with drift i.e. in case of presence of intercept in the model (Gujarati & Porter, 2009), the p-value is less than the significance level i.e. 0.0135<0.05 and even the absolute value of test statistic is greater than the absolute critical value (2.491>1.771). Thus, the null hypothesis is rejected at a drift level, and the data is now stationary.

The null hypothesis for **FDI** inflows too was rejected as the p-value is greater than the significance level i.e. 0.5283>0.05. Furthermore, the testing was done in case of drift and trend to determine the stationarity of the variable in the inclusion of intercept or deterministic term in the model (Gujarati & Porter, 2009). But here also the null hypothesis was rejected due to high significance value and low test-statistic value.

Finally, the first-order differentiated value of FDI inflows was tested and the null hypothesis of the unit root was rejected. The p-value was less than the significance level and the absolute test statistic value was also greater than the critical value i.e. 0.0061 < 0.05 and 3.584 > 3.000. Thus, the null hypothesis of non-stationarity was rejected. DiffFDI was generated to represent the stationary form of FDI inflows.

### Cointegration

Cointegration test studies the nature of the relationship between the variables. It determines whether there is any relationship or linkage between the variables or not. Existence of cointegration between the variables ensures that there is a linkage between the variables and no spurious or non-sense relationship is studied (Gujarati & Porter, 2009). Johansen cointegration results for testing the long-run relationship between **FDI** inflows and electrical conductivity is given below.

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

0 | 7.3800* | 15.41 | 4.3391 | 14.07 |

1 | 2.6053 | 3.76 | 3.0408 | 3.76 |

**represent significant at 5%level*

Table 2: Johansen cointegration test results

The above table shows that the null hypothesis of having no cointegration is not rejected for 0 ranks as the trace and max statistic value is less than the critical value i.e. 7.3800 < 15.41 and 4.3391 < 14.07 (Kumar & Chander, 2016). Thus, there exist 0 cointegrating vectors to represent the relationship between FDI inflows and electrical conductivity. Since trace statistic value was less than the critical value, a long-run linkage between the variables does not exist.

Furthermore, VECM (Vector Error Correction Model) test was applied to examine the short-run relationship between the variables (Azhagaiah & Banumathy, 2015; Zou, 2018). Results of the test are given below.

Cointegrating Equation Variable | Coefficient |
---|---|

LnConductivity | 1 |

DiffFDI | .6075883 |

Constant | -8.731208 |

Table 3: VECM test results

The coefficient value of DiffFDI represented in Table 5 is 0.6075883 thus depicting that there is an influence of **FDI **inflows on the Conductivity. Zou, (2018) stated that the coefficient value of the VECM test determines the short run movement of one variable due to other variables. Hence, short-run cointegrating equations can be formed using **FDI** inflows and conductivity.

### Normality

Presence of normally distributed data for deriving the relationship or studying the linkage is an important property of the classical linear regression model. Normality ensures that the dataset is symmetrical in nature and there is no skewness present. Thus it is essential to test the normality of the model (Casson & Farmer, 2014). Shapiro-Wilk test was performed to analyze the distribution of the dataset. Results for this test is given below.

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

LnConductivity | 0.25290 |

Difffdi | 0.50621 |

Table 4: Shapiro-Wilk test results

The p-value of conductivity and **FDI** inflows is greater than the significance level of the study i.e. 0.25290 and 0.50621 > 0.05 (Casson & Farmer, 2014). Thus, the null hypothesis of having a normal distribution of the dataset is not rejected. Furthermore, in the final model, the variables are normally distributed. The results could be computed to study the impact of **FDI** inflows on water pollution.

## Regression

Using the stationary, cointegrated, and normally distributed variable, the regression model for studying the impact is given below.

Wherein,

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

Dependent | Stationary form of Natural Log-transformation for average electrical conductivity level of Indian rivers at the t-time period | |

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

Coefficients | Intercept, Slope Coefficient | |

Error Term | Residual | |

T | Time |

Table 5: Variables used for regression

Results for the regression is given below.

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

Difffdi | -.6536039 | -3.45 | 0.004 | 0.4773 | 0.4371 |

Constant | 8.726713 | 119.18 | 0.000 |

Table 6: Regression results

R^{2} and Adjusted R^{2} values are 0.4773 and 0.4371. Even the p-value shows the value less than the significance level of the study. However, before testing the hypothesis, some more tests need to be performed to avoid the presence of bias in the results (Casson & Farmer, 2014).

The above figure shows that there is a significant impact of **FDI** inflows on the electrical conductivity level as the scatter plot of conductivity is close to the fitted line. However, some of the points are far from the fitted line. Thus, to increase the significance of the results and derive more appropriate results further diagnostic tests were performed on the residuals of the model.

## Autocorrelation diagnostic test

Linear regression can depict effective and reliable results only when the errors terms are not interdependent i.e. there is no autocorrelation present in the model. Autocorrelation of data is tested to validate the specification of the model and the effectiveness of the results (Huitema & Laraway, 2006). Durbin Watson test was applied and the results of this test are given below.

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

1.313278 | 0.946 | 1.543 | 2.457 | 3.054 |

Table 7: Durbin Watson result

The results in the above table show that the value of D-statistic lies between the D_{L} and D_{U} i.e. 0.946<1.313278<1.543. Thus, the value lies in the intermediate zone but close to the negative serial correlation.

Okumoko, Akarara, & Opuofoni, (2018) in their study stated that if the value of Durbin-Watson statistic is approximately 2, then there is no problem autocorrelation in the model. As the D-statistic value is far from 2, thus, the Cochrane-Orcutt AR (1) regression test (Wooldridge, 2002) needs to be applied to correct the autocorrelation.

The below table shows the result of the Cochrane-Orcutt AR (1) regression.

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

Difffdi | -.600818 | -3.15 | 0.008 | 0.4521 | 0.4065 |

Constant | 8.722442 | 79.19 | 0.000 |

Table 8: Cochrane-Orcutt AR (1) regression results for the final model

Durbin Watson test result for the Cochrane-Orcutt AR (1) regression is given below.

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

1.797450 | 0.905 | 1.551 | 2.449 | 3.095 |

Table 9: Durbin Watson result

The value of D-statistic lies
between the D_{U} and 4-D_{U }i.e. 1.551 < 1.797450 < 2.449,
and as stated by Okumoko, Akarara, & Opuofoni, (2018), the value of D-statistic is
close to 2, thus the problem of autocorrelation has been removed from the
study.

## Heteroscedasticity diagnostic test

Homoscedasticity is the important property of a linear regression analysis. However, sometimes the variance of the predicted values of regression doesn’t remain the same. This causes a decrease in the efficiency of the model and creating the problem of heteroscedasticity. Thus, to avoid misspecification of the model, heteroscedasticity is tested (Casson & Farmer, 2014; Salkind, 2007).

In order to determine the presence of heteroscedasticity in the model, Bartlett’s Periodogram based white noise heteroscedasticity test was applied for the Cochrane-Orcutt AR (1) regression model.

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

0.8075 | 0.5320 |

Table 10: Heteroscedasticity test results

The above table shows that as the p-value of the B-statistic is 0.5320 > 0.05, the significance level, thus the null hypothesis of no heteroscedasticity is not rejected. Thus, the model is homoscedastic.

**FDI** inflows have a negative impact on conductivity levels

Cochrane-Orcutt AR (1) regression model is used to test the hypothesis. Though the value of R^{2} and Adjusted R^{2} has decreased as compared to the final model, the problem of autocorrelation and heteroscedasticity does not exist in this model. The R^{2} value is 0.4521, thus showing that 45% variation in electrical conductivity is due to **FDI** inflows.

Faraway, (2014) stated that the R2 value greater than 0 determines that there is a linkage between the variables. The value close to 0.5 or 0.6 is very good in the case of social science, and as the value is close to 0.5, thus adequate variation is represented in the model. Furthermore, the p-value test depicts that as the value is 0.008 < 0.05, thus the null hypothesis of having no significant impact of **FDI** inflows on water pollution is rejected.

Seltman, (2018) stated that the p-value represents the probability of selecting the statistic when the hypothesis is true. According to Seltman, if the p-value is less than the significance level of the study, then the stated hypothesis is significant to derive the impact. Thus, as the p-value represented in Table 8 is less than the significance level, thus, the model is significant for deriving the impact of **FDI** inflows on electrical conductivity. Coefficient value reveals that with a 1% increase in **FDI** inflows, the electrical conductivity level decreases by 0.600818%.

the above figure shows that the predicted line is in downward sloping thus showing the existence of a negative relationship between **FDI** Inflows and electrical conductivity level. Furthermore, the scatter plot of conductivity is very close to the predicted line thus showing that a significant relationship can be derived by studying the above-stated model. Hence, **FDI** Inflows tends to decrease the level of water pollution by decreasing the conductivity of water bodies.

## Secondary studies corresponding the results of **FDI** and water conductivity levels

A study by Abdouli & Hammami, (2017) stated that environmental degradation of economies decreases with an increase in the economic growth of the country. Instead of accessing the direct linkage between **FDI** inflows and environment degradation, Abdouli and Hammami firstly studied the relationship between FDI inflows and economic growth and then via economic growth depicted the impact on environmental degradation.

Furthermore, Orubu & Omotor, (2011) stated that for directing economic growth towards environment quality improvement along with reducing organize water pollutants, it is required to implement stringent policies. In India along with focusing on implementing wastewater management treatment plants, strict rules and regulations are too enforced (Kamyotra & Bhardwaj, 2011; Sahasranaman & Ganguly, 2018). Water Quality Assessment Authority was formed in 2001 to implement priority based actions and control water pollution (OSEC, 2010).

#### References

- Abdouli, M., & Hammami, S. (2017). The Impact of FDI Inflows and Environmental Quality on Economic Growth: an Empirical Study for the MENA Countries.
*Journal of the Knowledge Economy*,*8*(1), 254–278. https://doi.org/10.1007/s13132-015-0323-y - Adhikari K., R., & R.K., A. (2013).
*An Introductory Study on Time Series Modeling and Forecasting Ratnadip Adhikari R. K. Agrawal*. https://doi.org/10.1210/jc.2006-1327 - Azhagaiah, R., & Banumathy, K. (2015). Long – Run and Short – Run Causality between Stock Price and Gold Price : Evidence of VECM Analysis from India.
*Management Studies and Economic Systems*,*1*(4), 247–256. https://doi.org/10.12816/0019391 - Bhateria, R., & Jain, D. (2016). Water quality assessment of lake water: a review.
*Sustainable Water Resources Management*,*2*(2), 161–173. https://doi.org/10.1007/s40899-015-0014-7 - Casson, R. J., & Farmer, L. D. M. (2014). Understanding and checking the assumptions of linear regression: A primer for medical researchers.
*Clinical and Experimental Ophthalmology*,*42*(6), 590–596. https://doi.org/10.1111/ceo.12358 - CPCB. (2008). Status of Groundwater Quality in India. In
*Central Pollution Control Board, Ministry of Environment and Forests*. - Faraway, J. J. (2014).
*Texts in Statistical Science Series, Linear Models with R*(M. Tanner, J. Zidek, & C. Chatfield, eds.). Taylor & Francis. - Fri, R. (1972). Parameters of Water Quality – Interpretation and standards.
*Journal of Milk and Food Technology*,*35*(12), 715–718. https://doi.org/10.4315/0022-2747-35.12.715 - Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). In
*Basic Econometrics*. - Hassan, T., Parveen, S., Bhat, B. N., & Ahmad, U. (2017). Seasonal Variations in Water Quality Parameters of River Yamuna, India.
*International Journal of Current Microbiology and Applied Sciences*,*6*(5), 694–712. https://doi.org/10.20546/ijcmas.2017.605.079 - Huitema, B., & Laraway, S. (2006). Autocorrelation.
*Encyclopedia of Measurement and Statistics*. - Kamyotra, J. S., & Bhardwaj, R. M. (2011). Municipal Wastewater Management in India.
*India Infrastructure Report*,*000*(mld), 299–311. - Kostakis, Sardianou, S. and, Lolos, I. and, & Eleni. (2016). Foreign direct investment and environmental degradation : Further evidence from Brazil and Singapore .
*MPRA*, (75643). - Kumar, V., & Chander, R. (2016). Foreign Direct Investment And Air Pollution : Granger Causality Analysis.
*IOSR Journal of Business and Management (IOSR-JBM)*, 12–17. - Nason, G. P. (2018). Stationary and non-stationary time series.
*Statistics in Volcanology*, (1994), 129–142. https://doi.org/10.1144/iavcei001.11 - Okumoko, T. P., Akarara, E. A., & Opuofoni, C. A. (2018). Impact of Foreign Direct Investment on Economic Growth in Nigeria.
*International Journal of Humanities and Social Science*,*8*(1). - Orubu, C. O., & Omotor, D. G. (2011). Environmental quality and economic growth: Searching for environmental Kuznets curves for air and water pollutants in Africa.
*Energy Policy*,*39*(7), 4178–4188. https://doi.org/10.1016/j.enpol.2011.04.025 - OSEC. (2010).
*Water & water treatment in India . Market opportunities for Swiss companies.* - Sahasranaman, M., & Ganguly, A. (2018).
*Wastewater Treatment for Water Security in India*. - Salkind, N. (2007). Heteroscedasticity and Homoscedasticity.
*Encyclopedia of Measurement and Statistics*, 8–10. https://doi.org/10.4135/9781412952644.n201 - Seltman, H. J. (2018).
*Experimental Design and Analysis*. - Wooldridge. (2002). Serial Correlation. In
*Introductory Econometrics*. - Zou, X. (2018). VECM Model Analysis of Carbon Emissions, GDP, and International Crude Oil Prices.
*Discrete Dynamics in Nature and Society*,*2018*. https://doi.org/10.1155/2018/5350308

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