The problem is to match violations of OLS assumptions to their consequences on the standard errors and coefficients of the regression model. The assumptions are Heteroskedasticity, Autocorrelation, Multicollinearity, and Non-normality. The possible consequences on the standard errors are that they are biased, and the possible consequences on the coefficients are that they are inefficient and/or inconsistent.

1. Problem Description

The problem is to match violations of OLS assumptions to their consequences on the standard errors and coefficients of the regression model. The assumptions are Heteroskedasticity, Autocorrelation, Multicollinearity, and Non-normality. The possible consequences on the standard errors are that they are biased, and the possible consequences on the coefficients are that they are inefficient and/or inconsistent.

2. Solution Steps

* Heteroskedasticity:

* Heteroskedasticity causes the standard errors to be biased.

* Heteroskedasticity does not cause coefficients to be biased or inconsistent, but it does cause them to be inefficient.

* Autocorrelation:

* Autocorrelation causes the standard errors to be biased.

* Autocorrelation does not cause coefficients to be biased or inconsistent, but it does cause them to be inefficient.

* Multicollinearity:

* Multicollinearity inflates the standard errors, thus making the coefficients inefficient. It does not cause the standard errors to be biased in a systematic way, but it can make them appear larger or smaller than they actually are.

* Multicollinearity doesn't cause the coefficients to be biased or inconsistent.

* Non-normality:

* Non-normality, especially in small samples, can lead to unreliable inference.

* In large samples, due to the Central Limit Theorem, even if the error term is non-normal, the OLS estimators are still approximately normally distributed. Therefore, with a large sample size, inference can still be approximately valid. However, in small samples, if the error term is not normally distributed, the OLS estimators are no longer normally distributed, and the usual hypothesis tests are not valid. Specifically, non-normality does not cause bias or inconsistency. However, in small samples, inference may be inaccurate.

* Non-normality doesn't affect standard error and coefficients in large samples.

3. Final Answer

* Heteroskedasticity causes biased standard errors and inefficient coefficients.

* Autocorrelation causes biased standard errors and inefficient coefficients.

* Multicollinearity causes biased standard errors and inefficient coefficients.

* Non-normality causes biased standard errors and inefficient coefficients.