ECON203 Final Exam - Econometrics | Practice Test / Quiz / MCQs

1. Consider the model: Earnings = β₁ + β₂ Schooling + β₃ Age + u.
The standard errors appear in parentheses. Cov(Age, Schooling) = 0.47. The first column of the table gives the result of a multiple regression on Schooling and Age. The estimated coefficients for the multiple regression model are both significantly different from zero at a very high significance level. The second and third columns are regressions with one variable only. What could be one reason that the coefficient on schooling in the second column is greater than that in the first column?

The coefficient is subject to omitted variable bias.The coefficient is subject to multicollinearity.The variable 'Age' is not an important factor in the model for earnings.Schooling is an important factor, and it is important to see its effect in exclusion.

2. Which of the following is a possible consequence of the regressors being stochastic, (i.e., the observations of the regressors in the sample are not fixed and given, rather, they are drawn randomly from fixed populations with finite means and finite population variances)?

The disturbance term may not have a zero expectation.The regressors are all correlated such that the possibility of multicollinearity is very high.The specification of the model when the regressors are randomly selected from fixed populations necessarily are non-linear.The disturbance term may not be independent of the regressors so that it is possible for the regressors and the disturbance term to have a distributional relationship between them.

3. Suppose we have the following simple regression model with AR(1) disturbance:

, where

and

is assumed to follow the OLS assumptions of zero expected value, constant variance, and no autocorrelation. The following algebra describes the steps that can eliminate the problem of AR(1) autocorrelation. Which of the answer choices explain why there is no autocorrelation in the equation resulting in the last step?
Step 1: What holds true at time 't' also holds true at time

.
Step 2: Multiply both sides by p:

.
Step 3: Subtract the equation in step 2 from the original equation to get an equation free of autocorrelation:

or rewrite as:

, where =

The last equation takes into account the past values of the variables, thus eliminating autocorrelation.The disturbance term ε_t is independently distributed and satisfies all OLS assumptions, so the equation is free of autocorrelation.The coefficients now take into account the value of ρ, and thus autocorrelation is eliminated.There is no multicollinearity in the last equation which is why it is free of autocorrelation.

4. You are given the following data:
RSS₁ based on first 15 observations = 75, df = 10;
RSS₂ based on last 15 observations = 278, df = 10.
The critical F value for 10 numerator and 10 denominator df at the 5% level is 2.98. What would you conclude about heteroscedasticity in this case?

Nothing can be said unless more information is provided.The Goldfeld-Quandt test confirms the presence of heteroscedasticity in this case.Both the White test and the Goldfeld-Quandt test confirm that there is no heteroscedasticity in this case.The White test confirms the presence of heteroscedasticity in this case.

5. Which of the following is likely to occur as a result of multicollinearity?

The variances of coefficients are very small.The coefficients are biased.The t-statistics are very high.The t-ratio of one or more coefficients is statistically insignificant, although the F-test for their joint explanatory power is highly significant.

6. In a situation where heteroscedasticity is suspected, but there is not enough information to identify its nature, how can one overcome the problem of biased standard errors?

Refine the data to get homoscedastic variances, otherwise the results are contaminated and misleading.Run a standard OLS regression, ignoring heteroscedasticity, because in large samples, this problem is not of any consequence and the t-tests and F-tests are asymptotically valid.Use White's heteroscedasticity-consistent variances and standard error at least in large samples, in which the t-tests and F-tests are asymptotically valid.Use weighted least squares, i.e. transform the model by using appropriate weights for the regression model so that the error variance becomes homoscedastic.

7. Consider the multiple regression model: EARNINGS = β₁ + β₂ HEIGHT + β₃EDUCATION + β₄EXPERIENCE + u. What test would you perform if you wished to test the following null hypothesis?

A one sided t-testA two-sided t-testNot enough information is provided to make the conclusion.An F-test

8. For the model Y_t = β₁Y_t-1+ u_t, if β₁ = 1, would the model be stationary or non-stationary and what would the model be referred to as?

It would be stationary and referred to as an integrated model.It would be non-stationary and referred to as Random walk.It would be non-stationary with a deterministic trend.It would be stationary and referred to as random walk with drift.

9. Which of the following does NOT occur as a result of autocorrelation?

OLS is unbiased and efficient and therefore the preferred choice for estimation.The regression coefficients remain unbiased.Autocorrelation causes the standard errors to be estimated wrongly, often being biased downwards.OLS estimators are biased if the disturbance term is subject to autocorrelation.

10. Consider the model given by ln Y = β₁ + β₂ ln X₂ + β₃ ln X₃ + β₄ ln X₄ + u, where Y = per capita consumption of tea, X₂ = real disposable per capita income (measured in dollars), X₃ = price of sugar (measured in dollars per pound), X₄ = price of coffee (measured in dollars per pound). Suppose that according to economic theory, coffee and tea are competing products. What would be the sign of the coefficient β₄?

β₄ < 0β₄ = 0β₄ > 0This cannot be determined with the amount of information given.

11. Which of the following describes one of the statistical properties of the OLS estimators?

They are efficient estimators or minimum-variance unbiased estimators.They are unbiased but do not necessarily have minimum variance.They are not necessarily consistent.They are minimum variance but biased estimators.

12. A variable Y depends upon some explanatory variables X₂…..X_k in the following manner: Y = β₁ + β₂ X₂ + β₃X₃ +…+ β_k X_k + u.
If for some reason, there is no data available on a certain variable, say X₃, and a proxy variable Z that is linearly related to X₃ is used instead, then X₃ = µ + αZ.
The regression model is now rewritten as:
Y = β₁ + β₂ X₂ + β₃(µ+αZ)β₄ X₄ +…+ β_k X_k + u
= (β₁ + β₃µ) + β₂ X₂ + β₃αZ + β₄X₄+…+ β_k X_k + u
What are the consequences of including a proxy variable as shown above?

R2 of the model with a proxy variable changes compared to the true model.The result of including a proxy variable is no different than estimating the model if data were available on X₃ except that with the proxy variable, it will not be possible to estimate the individual coefficientsβ₁ and β₃.The standard errors and t-statistics of all coefficients will be different if a proxy variable is included.The estimates of all coefficients in the model will be different if a proxy variable is included.

13. Suppose an economist is trying to determine the following model: Ln wage = β₀ + β₁education + u. According to the economist, the error term includes 'ability,' an unobserved explanatory variable, which is correlated with education. He then seeks to find another variable for this model such that this new variable is uncorrelated with ability but correlated with education. What type of variable is the economist employing in estimating this model?

A proxy variableA dummy variableAn instrument variableA binary dependent variable

14. Consider the model given by the following equation.
What is the best way to mitigate the problem of interactive terms?

Omit the interactive term, because excluding it will not change the results much.Assume that one of the two is constant and then run the regression.Rescale X₂ and X₃ so that they are measured from their sample means.Run a regression of X₂ on X₃ (or vice versa) and include the results in the above regression.

16. Consider the following system of simultaneous equations representing the demand-and-supply model:
Q_s = β₁ + β₂P +u₁ and Q_d =α₁ +α₂P+α₃I +u₂, where Q_s and Q_d are the quantities supplied and demanded respectively, P = price of the commodity, and I = income. Which of these equations are identified, i.e. which of these can be estimated?

The demand function is identified, but the supply function is not.Both are identified.Neither is identified.The supply function is identified, but the demand function is not.

17. Assume Y represents the number of slices of bread consumed per person, per day. X represents the price of one pound of bread, measured in dollars. Z represents the income of the consumer. A two variable linear model is computed from the data available, and the result is given as follows:

. The R-square for the model is found to be R^₂ = 0.5972. What is the interpretation of R-square?

If the price of one pound of bread goes up by a dollar, 60 percent of the daily consumption of bread per person is affected.About 40 percent of the variation in per person daily bread consumption is explained by the variation in the consumer's income.About 60 percent of the bread is consumed by an individual daily.About 60 percent of the variation in per person daily bread consumption is explained by the variation in the retail price of bread.

18. Which of the following is true of the instrumental variables (IV) estimator?

The IV estimator is biased and inconsistent.The IV estimator is unbiased and consistent.The IV estimator is unbiased but inconsistent.The IV estimator is biased but consistent.

19. The formula for

What is the relationship between R² and the least squares principle to determine the parameters in the model?

The OLS regression coefficients are chosen such that the sum of the squares of the residuals is minimized.Goodness of Fit is maximized when the sum of the squares of the residuals is maximized.The OLS regression coefficients are chosen such that the sum of the squares of the residuals is minimized.Goodness of Fit is also maximized when the sum of the squares of the residuals is minimized.The OLS regression coefficients are chosen such that the sum of the squares of the residuals is maximized.Goodness of Fit is also maximized when the sum of the squares of the residuals is maximized.The OLS regression coefficients are chosen such that the sum of the squares of the residuals is minimized.Goodness of Fit is minimized when the sum of the squares of the residuals is minimized.

20. Which of the following is NOT an advantage of panel data over cross-section data?

The problem of bias caused by unobserved heterogeneity is removed in panel data.They are relatively inexpensive compared to cross-section data.They are less susceptible to measurement error.Panel data is often large in comparison to cross-section data.

21. Which of the following is NOT a possible measure for alleviating the multicollinearity problem?

Dropping one of the collinear variablesDecreasing the number of observationsCombining the correlated variablesCombining cross-sectional and time-series data

22. Which of the following explains the Central Limit Theorem?

The sample means will approximate a normal distribution as the sample size becomes large, only if the underlying population distribution is normal.Irrespective of the sample size, the distribution of the sample mean will always approximate a normal distribution.If the underlying population distribution is not normal, the distribution of sample means cannot approximate a normal distribution, even if the sample size becomes large.The distribution of sample means will approximate a normal distribution as the sample size becomes large, even if the underlying population distribution is not normal.

24. A person committed a legal crime and was taken to trial. However, due to lack of evidence, he was proved 'not guilty' and was not charged for the offense. If we consider the null hypothesis to be 'guilty,' this scenario represents which of the following?

A Type I error was made.Both Type I and Type II errors were made.Neither Type I nor Type II error was made.A Type II error was made.

25. Which of the following is NOT a shortcoming of the linear probability model?

The OLS estimation of the linear probability model may predict probabilities of more than 1 or less than 0.The disturbance terms are not normally distributed, and hence the standard errors and test statistics are invalid.The distribution of the disturbance terms is continuous.The variances of the disturbance terms are heteroscedastic.

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25 Questions

❤ If you liked Fatskills, consider supporting us by checking out The Life Manuals You Never Got.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know? Privacy | Terms |

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All trademarks, logos and brand names are the property of their respective owners. All company, product and service names used in this website are for identification purposes only. Use of these names, trademarks and brands does not imply endorsement.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know?
Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson
© 2026 Fatskills.com