Answer to Question #264326 in Economics for lilu

Question

What are the implications of high multicollinearity for the OLS estimators of slope coefficients in Multiple Linear Regression model and their variances?

Answer 1

Signs of multicollinearity.

(1) In a model with two variables, one of the signs of multicollinearity is the value of the pair correlation coefficient close to one. If the value of at least one of the pair correlation coefficients is greater than 0.8, then multicollinearity is a serious problem. However, in a model with more than two independent variables, the pairwise correlation coefficient can take on a small value even in the case of multicollinearity. In this case, it is better to consider the partial correlation coefficients. 2. To check multicollinearity, we can consider the determinant of the matrix of pair correlation coefficients | r |. This determinant is called the correlation determinant | r | ∈ (0; 1). If | r | = 0, then there is complete multicollinearity. If | r | = 1, then there is no multicollinearity. The closer | r | to zero, the more likely the presence of multicollinearity.

3. If the estimates have large standard errors, low significance, but the model as a whole is significant (has a high coefficient of determination), then this indicates the presence of multicollinearity.

4. If the introduction of a new independent variable into the model leads to a significant change.

19. Dummy variables: definition, purpose, types (specification, meaning of a parameter for a dummy variable). A dummy variable is a qualitative variable that takes values ​​0 and 1 and is included in an econometric model to take into account the effect of qualitative features and events on explained variable. At the same time, dummy variables make it possible to take into account the influence of not only qualitative attributes that take two but also several possible values. In this case, several dummy variables are added.

In some cases, when the quality of the models is improved, it becomes necessary to assess the influence of qualitative characteristics on the endogenous variable (for example: for the function of demand, this is the taste of the consumer, age, seasonality).