Question

Consider the following two models: Model 1:y y=α+β

1
​
x+β
2
​
w+ε
1
​
Model 2: y=α+β
1
​
x+β
2
​
z+ν
t
​
where w=5x+3 and z=x
2
. For both models indicate if they can or can not be estimated using OLS. If not, explain which assumption is violated

Answer 1

Model 1 can be estimated using ordinary least squares (OLS). Since it meets the assumptions required for OLS regression analysis: linearity, homoscedasticity, normality of errors, and independence of error terms.

However, Model 2 can not be estimated using OLS because it violates the assumption of constant variance of errors (homoscedasticity). The variable "z" is generated by multiplying x by a factor of two, resulting in larger variability around the mean compared to "w". Therefore, it is essential to check the underlying distribution of residuals and verify that they conform to the model assumptions before conducting any further analyses. Violating this assumption may lead to biased parameter estimates, inefficient estimators, and reduced confidence intervals. Potential remedies include transforming variables, weighting observations, applying diagnostic tests, and employing robust estimation techniques.