Level of dissolved oxygen has been identified as a composite indicator of water pollution in the previous article. It represents the trophodynamics and water quality of the aquatic system. A level close to the saturation point i.e. 4.8 mg/L is the minimum level of oxygen required for a healthy aquatic environment. Fall of oxygen concentration below this level leads to the death of aquatic species.

Some of the factors leading to disturbance in dissolved oxygen levels are:

- nitrification,
- rate of respiration,
- mineralization, and
- nature of the soil and sewage discharge (Prasad et al, 2014).

## Presence of dissolved oxygen in major Indian rivers

Studies by Basavaraddi, Kousar, Puttaiah (2012) & Kale (2016) have shown that other than certain natural factors, human-related factors too contribute to reduced dissolved oxygen levels in water bodies.

Shivalik Himalayan stream has a dissolved oxygen level below 4 mg/L in early hours of the summer season. Whereas Ganga stream in Kanpur has shown a maximum dissolved oxygen level of 13 mg/l in the summers. While, the minimum level was 3.5 mg/l (Gautam & Sharma, 2011; Naseema, Masihur, & Husain, 2013).

The below figure shows the variation in the average level of dissolved oxygen in various Indian rivers for the period of 2002-2017. The graph shows that with time the dissolved oxygen level has been increasing and the highest level was recorded in 2012 of approximately 9 mg/L.

The aim of this article is to determine the impact of *Foreign Direct Investment (FDI)* inflows on dissolved oxygen levels in India. This will help to establish how FDI inflows are leading to water pollution in India. For this purpose, data from 15 major Indian rivers were collected for the time period 2007-2017. The data on water pollution indicators were obtained from the Government websites of National Water Mission and Ministry of Statistics and Programme Implementation.

## The hypothesis to determine the impact

The first step in a time series analysis is to check the data for variability. According to Lütkepohl & Xu, (2009), the, natural log transformation of the variable can be used to stabilize the dataset. The variability in the dataset for this study 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. Dissolved oxygen has been used as an indicator of water pollution and further, the impact of *FDI* inflow is determined using the log-log transformed model.

Further, to determine the impact of net *FDI* inflows on dissolved oxygen levels, the following hypothesis was framed.

H_{0}:There is no significant impact of FDI inflows on the level of dissolved oxygen in Indian rivers.

H_{A}:There is a significant impact of FDI Inflows on the level of dissolved oxygen in Indian rivers

## Diagnosing stationarity in the time series data

Stationarity in a dataset means that the value of their mean and variance is constant across time. This assumption helps in determining the relationship reliably and forecasting (Adhikari K. & R.K., 2013; Gujarati & Porter, 2009; Nason, 2018).

Stationarity of the dataset was tested using the Augmented Dickey-Fuller test in STATA. The table below represents the results of the Augmented Dickey-Fuller test.

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

LnDO | -2.017 | -3.000 | 0.2791 |

LnDO with drift | -2.017 | -1.771 | 0.0324 |

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: Augmented Dickey-Fuller test results

For dissolved oxygen, the absolute value of test statistic is less than the critical value i.e. 2.017 < 3.000. The p-value of the variable too is greater than the significance level of the study i.e. 0.2791 > 0.05. Thus the null hypothesis of having unit root with zero intercept is not rejected.

Furthermore, the dissolved oxygen variable is considered in case of drift. This drifted value helps in testing whether stationarity is present in the presence of intercept in the model (Gujarati & Porter, 2009). The drifted value of dissolved oxygen has the p-value < significance level i.e. 0.0324 < 0.05. Thus, the null hypothesis of having unit root is rejected and LnDO is now stationary.

In the case of FDI, initially the absolute value of test statistic is less than the absolute critical value. Moreover, the p-value is greater than the significance level of the study. Thus, the null hypothesis of having a unit root with zero intercepts is not rejected.

Furthermore, the testing is done in case of drift and trend to check the stationarity in presence of the intercept and deterministic trend (Gujarati & Porter, 2009) but the absolute test statistic value is less than the absolute critical values (i.e. 1.511<3.000 and 1.511M<1.771). Thus the null hypothesis is still not rejected.

Finally, the first order differenced variable was tested, and the p-value of *FDI* is 0.0061 < 0.05. The absolute test statistic value is also greater than the critical value. Hence, the null hypothesis is rejected, and the stationary form of LnFDI is derived. The absolute value of the test statistic is greater than the absolute critical value of *FDI *inflows for first-order differentiation. Thus the stationarity is derived at first level. DiffLnFDI was generated to represent first-order differentiation.

## Checking relationships between the variables

Cointegration test is used to determine whether there exists any relationship or linkage between the variables or not. This helps to analyse the related variables. This condition is tested before the regression analysis (Gujarati & Porter, 2009).

Johansen cointegration test was applied to study the long-run relationship between *FDI* inflows and dissolved oxygen. The results are shown in the below table.

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

0 | 13.3315* | 15.41 | 10.7261* | 14.07 |

1 | 2.6053 | 3.76 | 2.6053 | 3.76 |

*significant at 5% level

Table 2: Johansen Cointegration Test Results

The null hypothesis of having no cointegration is not rejected at 0 ranks i.e. value of trace statistic and max statistic > critical value (13.3315 < 15.41 and 10.7261 < 14.07). Thus, there exist 0 cointegrating vectors for representing the long-run impact of *FDI* inflows on dissolved oxygen.

Kumar & Chander, (2016) also studied the impact of FDI inflows on environmental pollution and stated that the decision of cointegration is based on comparing the trace statistic and max. statistic value with their critical values. As the trace statistic is greater than the critical values, thus long-run linkage between the variables exist and change in one variable do impact the other. However, as the results in Table 2 show that there is 0 cointegrating vector (max. rank), the long-run movement among the variables do not exist.

For studying the short-run impact, Vector Error Correction Model (VECM) test was applied (Azhagaiah & Banumathy, 2015; Zou, 2018). Below table represents the results of the VECM model.

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

LnDO | 1 |

DifflnFDI | .2255285 |

Constant | -2.049292 |

Table 3: VECM model Results

The above table shows that the coefficient value of DifflnFDI is 0.2255285 i.e. greater than 0, thus there is a positive influence of FDI inflows on the dissolved oxygen levels. The coefficient value depicts the movement of one variable with the other on a short term basis (Zou, 2018). Hence, short-run cointegration exists between *FDI* inflows and dissolved oxygen.

## Diagnosing if the data is normally distributed

A normally distributed dataset states that there exists symmetrical distribution of the data across time. Presence of normality in a dataset is not only an assumption of linear regression but also helps in deriving the effective results. Hence, before performing a regression analysis between *FDI* and water pollution, normality is tested (Casson & Farmer, 2014). Shapiro-Wilk test determines the distribution of LnDo and DifflnFDI. The results of the test are shown below.

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

LnDO | 0.11951 |

Difflnfdi | 0.50621 |

Table 4: Shapiro-Wilk Test results

The above table shows that the p-value of the variables is greater than the significance level of the study i.e. 0.11951 and 0.50621 > 0.05 (Kostakis et al., 2016). Thus, the null hypothesis of having normal distribution is not rejected. Hence, the dataset of the variables is normally distributed. Hence, as normality exists in the dataset of both the variables, the regression analysis can be performed.

## Regression analysis

The stationary, cointegrated, and normally distributed variables were used to frame the regression model i.e.

Wherein,

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

Dependent | Stationary form of Natural Log-transformation for average dissolved oxygen level of Indian rivers at 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 Description of Regression Equation

Below table represents the results of the regression.

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

Difflnfdi | -.0765638 | -1.57 | 0.141 | 0.1589 | 0.0942 |

Constant | 2.029979 | 107.67 | 0.000 |

Table 6: Regression results of Final Model

The above table shows that the p-value of Difflnfdi is 0.141 > 0.05, the significance level of the study. Though the R2 and Adjusted R2 value are 0.1589 and 0.0942, still, the presence of biases in the results needs to be tested (Casson & Farmer, 2014).

The above figure shows that the values of difflnfdi are scattered away from the fitted line depicting very less impact of *FDI* inflows on the dissolved oxygen levels. Though the direction of the effect is somehow decreasing no adequate result about the impact could be determined.

## Autocorrelation test

Autocorrelation refers to the existence of the relationship between the error terms in the model. No autocorrelation is an assumption of linear regression, and even valid results can be derived in the absence of autocorrelation. Thus, autocorrelation is tested before interpreting the results of the model (Huitema & Laraway, 2006).

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

1.134379 | 0.946 | 1.543 | 2.457 | 3.054 |

Table 7: Durbin Watson Results

The above table shows that though the value lies in the indeterminate zone i.e. between DL and DU but the value is close to the DL value. Hence, there is a probability of having a negative serial correlation.

Furthermore, as stated by Okumoko, Akarara, & Opuofoni, (2018), the value of Durbin Watson statistic needs to be close to 2 for having no autocorrelation in the model. As the value is far away from the stated level, thus the problem needs to be corrected. Therefore, in order to remove the problem of serial correlation, Cochrane-Orcutt AR(1) regression was applied (Wooldridge, 2002).

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

Difflnfdi | -.0364019 | -0.87 | 0.402 | 0.0593 | -0.0191 |

Constant | 2.023968 | 56.35 | 0.000 |

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

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

1.709483 | 0.905 | 1.551 | 2.449 | 3.095 |

Table 9: Durbin Watson Result

Now, that the problem of autocorrelation has been removed from the model as the value of D-statistic is between D_{U} and 4-D_{U} i.e. 1.551<1.709483<2.449. The value of Durbin Watson statistic is now close to 2, thus fulfilling the condition stated by Okumoko, Akarara, & Opuofoni, (2018) for having no autocorrelation in the model.

## Heteroscedasticity

Heteroscedasticity is the condition of having a different variance for all the predicted values of the regression. As the linear regression need to be homoscedastic for deriving reliable results, thus heterogeneity is tested (Casson & Farmer, 2014; Salkind, 2007).

Bartlett’s Periodogram based white noise heteroscedasticity test results for the new Cochrane-Orcutt AR (1) regression model are shown below.

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

1.2540 | 0.0861 |

Table 10: Heteroscedasticity Test results

The p-value of the test results is greater than the significance level i.e. 0.0861>0.05. Thus the null hypothesis of no heteroscedasticity is not rejected. Hence, the model is homoscedastic. Kostakis et al., (2016) in their study showed that the greater p-value ensures that the model is free from the problem of heteroscedasticity.

## FDI has no impact on the dissolved oxygen levels in Indian rivers

The final model derived by Cochrane-Orcutt AR (1) regression, is free from the problem of autocorrelation and heteroscedasticity. Table 8 shows that the value of R^{2} and adjusted R^{2 }has decreased i.e. from 0.1589, the R^{2} value is now 0.0593. This represents that only 5% of the variation in the dissolved oxygen is represented by the *FDI *inflows of India for the period of 2002-2017. The above figure also shows that the scatter plot of dissolved oxygen is very far from the predicted line. The direction of the line also shows almost constant relationship thus depicting not much impact of *FDI* inflows. Hence, *FDI* inflows does not have significant contribution in influencing dissolved oxygen level in Indian Rivers.

Faraway, (2014) stated that for social science-based studies 0.6 R^{2} stated good linkage between the factors. Thus, the variation level represented by dissolved oxygen is very less. Further, p-value test shows that still, the value is greater than the significance level i.e. 0.402>0.05. Seltman, (2018) stated that if the value is less than the significance level of the study, then there is significance in studying the stated hypotheis. As the p-value for the model is high, thus, the null hypothesis of having no significant impact of *FDI* inflows on dissolved oxygen level is not rejected. Hence, *FDI* does not have an impact on dissolved oxygen levels in river water in India.

## Studies correlating the findings of the impact of FDI on dissolved oxygen

A study by Zomorrodi & Zhou, (2017) studied the impact of *FDI* on the environment quality by focusing on air and water quality in China. The analysis suggests that though there is a significant impact of *FDI* inflows on Sulphur dioxide (air quality indicator) but no such relationship exists for water quality. Water pollutant emissions are not associated with *FDI* inflows. Mainly the factors which affect the water quality is industrial effluents, defecation, and sewage water discharge. Hence, the quality of water degrades by the discharge of industrial effluents mainly from manufacturing industries which are also the largest source of attracting *FDI *inflows (Hassaballa, 2013; RBI, 2018). But there is no direct significant linkage between *FDI* inflows and water pollution.

#### References

- 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 - Basavaraddi, S. B., Kousar, H., & Puttaiah, E. T. (2012). Dissolved Oxygen Concentration – a Remarkable Indicator of Ground Water Pollution in and around Tiptur town, Tumkur District, Karnataka, India.
*Bulletin of Environment, Pharmacology & Life Sciences*,*1*(3), 48–54. Retrieved from www.bepls.com - 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 - Faraway, J. J. (2014).
*Texts in Statistical Science Series, Linear Models with R*(M. Tanner, J. Zidek, & C. Chatfield, eds.). Taylor & Francis. - Gautam, D. K., & Sharma, M. R. (2011). Effect of pollution of dissolved oxygen concentration in seer stream of Shivalik Himalayas.
*Indian Journal of Environmental Protection*,*31*(6), 464–466. - Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). In
*Basic Econometrics*. - Hassaballa, H. (2013). Environment and Foreign Direct Investment : Policy Implications for Developing Countries.
*Journal of Emerging Issues in Economics, Finance\ and Banking*,*1*(2), 75–106. - Huitema, B., & Laraway, S. (2006). Autocorrelation.
*Encyclopedia of Measurement and Statistics*. - Kale, V. (2016). Consequence of Temperature, pH, Turbidity and Dissolved Oxygen Water Quality Parameters.
*International Advanced Research Journal in Science, Engineering and Technology ISO*,*3297*(8), 186–190. https://doi.org/10.17148/IARJSET.2016.3834 - 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. - Naseema, K., Masihur, R., & Husain, K. A. (2013). Study of seasonal variation in the water quality among different ghats of river Ganga, Kanpur, India.
*Journal of Environmental Research And Development*,*8*(1). - 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). - Prasad, B. S. R. V., Srinivasu, P. D. N., Varma, P. S., Raman, A. V., & Ray, S. (2014). Dynamics of Dissolved Oxygen in Relation to Saturation and Health of an Aquatic Body: A Case for Chilka Lagoon, India.
*Journal of Ecosystems*,*2014*(February), 1–17. https://doi.org/10.1155/2014/526245 - RBI. (2018).
*Foreign Direct Investment Flows To India : Country Wise and Industry Wise*. - 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). SerialCorrelation. In
*Introductory Econometrics*. - Zomorrodi, A., & Zhou, X. (2017). Impact of FDI on Environmental Quality of China.
*International Journal of Business, Economics and Management*,*4*(1), 1–15. https://doi.org/10.18488/journal.62/2017.4.1/62.1.1.15 - 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

- How to write the introduction of a research paper? - July 7, 2020
- What is null and alternative hypothesis? - June 19, 2020
- Understanding various hypothesis testing steps - June 17, 2020

## Discuss