, PLEASE USE THIS DOCUMENT AS A GUIDE TO ANSWER YOUR ASSIGNMENT
Question 1
1.1. Explain the concept of omitted variable bias and distinguish between positive and negative
bias.
Omitted variable bias arises in a regression analysis when a key explanatory variable—one that
affects the dependent variable—is not included in the model. For this bias to occur, the omitted
variable must also be correlated with one or more of the variables that are included. Leaving it out
results in biased and unreliable coefficient estimates, which misrepresent the actual relationships.
A positive bias indicates the coefficient is exaggerated and appears larger than it truly is.
A negative bias implies the coefficient is underestimated—it may appear smaller than it should
be or even have the incorrect sign.
1.2. Explain in your own words how you test serial correlation with strictly exogenous variables.
When the regressors are strictly exogenous, meaning they are not related to past, present, or future
error terms, we can appropriately test for serial correlation (i.e. autocorrelation in the residuals) using
tools like the Durbin-Watson test or the Breusch-Godfrey test. Serial correlation occurs when error
terms are linked over time, which breaks the assumption that errors are independent. Because strict
exogeneity ensures no correlation between the explanatory variables and the errors at any time, these
tests can reliably identify whether serial correlation is present.
1.3. Explain, in your own words, the concept of heteroscedasticity and implications for
inferences in econometrics.
Heteroscedasticity occurs when the error terms in a regression model have unequal variance across
observations, breaking a fundamental assumption of the classical linear regression framework. When
this condition exists:
The Ordinary Least Squares (OLS) estimators remain unbiased,
However, the standard errors become inaccurate, leading to unreliable statistical tests such as
t-tests and F-tests,
As a result, confidence intervals and overall inferences drawn from the model may be
misleading.
Question 1
1.1. Explain the concept of omitted variable bias and distinguish between positive and negative
bias.
Omitted variable bias arises in a regression analysis when a key explanatory variable—one that
affects the dependent variable—is not included in the model. For this bias to occur, the omitted
variable must also be correlated with one or more of the variables that are included. Leaving it out
results in biased and unreliable coefficient estimates, which misrepresent the actual relationships.
A positive bias indicates the coefficient is exaggerated and appears larger than it truly is.
A negative bias implies the coefficient is underestimated—it may appear smaller than it should
be or even have the incorrect sign.
1.2. Explain in your own words how you test serial correlation with strictly exogenous variables.
When the regressors are strictly exogenous, meaning they are not related to past, present, or future
error terms, we can appropriately test for serial correlation (i.e. autocorrelation in the residuals) using
tools like the Durbin-Watson test or the Breusch-Godfrey test. Serial correlation occurs when error
terms are linked over time, which breaks the assumption that errors are independent. Because strict
exogeneity ensures no correlation between the explanatory variables and the errors at any time, these
tests can reliably identify whether serial correlation is present.
1.3. Explain, in your own words, the concept of heteroscedasticity and implications for
inferences in econometrics.
Heteroscedasticity occurs when the error terms in a regression model have unequal variance across
observations, breaking a fundamental assumption of the classical linear regression framework. When
this condition exists:
The Ordinary Least Squares (OLS) estimators remain unbiased,
However, the standard errors become inaccurate, leading to unreliable statistical tests such as
t-tests and F-tests,
As a result, confidence intervals and overall inferences drawn from the model may be
misleading.
