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The purpose of this paper is to evaluate the association between inequality in energy intensity and social inequality in Indian cities, as these are the two predominant constituents of inequality in Indian socio-economic scenario. This study uses a bivariate cointegration based error correction model for assessing the causal association between the two inequality parameters, which are derived by using Theil's second measure. Given the sustainable development objective set by the government of India, interaction between these two parameters may prove out to be significant for achievement of this objective. It has been hypothesized that nature of this interaction varies largely based on the nature of the cities, i.e. semi-urban, urban, and metropolitan. The analysis has been done on the full and segregated dataset to visualize how the interaction changes with the nature of the cities. For analysis purpose, data for 139 Indian cities for the period of 2001-2013 have been selected. From the data of income, population, and energy consumption, two parameters of this study have been designed by using Theil's second measure. The analysis starts with checking the cross sectional dependence for both of the parameters. Subsequently, the stationarity of the data has been checked by using first generation unit root tests. Then, by employing the cointegration and error correction framework, the long run causal association has been assessed. For checking the short run causal association, Granger causality method has been applied. The data for this study have been collected form Ministry of Power, Govt. of India, Central Statistical Organization, India, and Census, India. Major findings of this study are, (a) for both the parameters and three segments, cross sections are independent, (b) the parameters are stationary at first difference, (c) there is long run cointegration relationship between them, and (d) the causal link between inequality in energy intensity and social inequality is unidirectional for the case of semi-urban cities, and it is bidirectional for the case of metropolitan and urban cities. For full dataset, causal link between inequality in energy intensity and social inequality is unidirectional. The Theil indices calculated for both the parameters show the trends of rising inequality for all the cities taken together. However, no significant trend was visualized for the individual strata of cities, for both of the parameters under consideration. This study summarizes that the economic growth achieved by India is not sustainable in nature. It can be achieved only by considering an inclusive growth framework, where social development will complement the growth objectives. Therefore, the fossil-fuel based economic growth agenda needs reconsideration, viewing the social dimensions of the cities. [ABSTRACT FROM AUTHOR]