What is the effect of heteroscedasticity?
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An important assumption of OLS is that the disturbancesμiappearing in the population regression function are homoscedastic (Error term have same variance)
.i.e. The variance of each disturbance termμi, conditional on the chosen values of explanatory variables is some constant number equal to$\sigma^2$. $E(\mu_{i}^{2})=\sigma^2$; where$i=1,2,\cdots, n$.Homo means equal and scedasticity means spread.Consider the general linear regression model\[y_i=\beta_1+\beta_2 x_{2i}+ \beta_3 x_{3i}+\cdots + \beta_k x_{ki} + \varepsilon\]If $E(\varepsilon_{i}^{2})=\sigma^2$ for all$i=1,2,\cdots, n$ then the assumption of constant variance of the error term or homoscedasticity is satisfied.If $E(\varepsilon_{i}^{2})\ne\sigma^2$ then assumption of homoscedasticity is violated andheteroscedasticity is said to be present. In case of heteroscedasticity the OLS estimators are unbiased but inefficient.
.i.e. The variance of each disturbance termμi, conditional on the chosen values of explanatory variables is some constant number equal to$\sigma^2$. $E(\mu_{i}^{2})=\sigma^2$; where$i=1,2,\cdots, n$.Homo means equal and scedasticity means spread.Consider the general linear regression model\[y_i=\beta_1+\beta_2 x_{2i}+ \beta_3 x_{3i}+\cdots + \beta_k x_{ki} + \varepsilon\]If $E(\varepsilon_{i}^{2})=\sigma^2$ for all$i=1,2,\cdots, n$ then the assumption of constant variance of the error term or homoscedasticity is satisfied.If $E(\varepsilon_{i}^{2})\ne\sigma^2$ then assumption of homoscedasticity is violated andheteroscedasticity is said to be present. In case of heteroscedasticity the OLS estimators are unbiased but inefficient.
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