Econometrics Ketevani Kapanadze
Active Learning
a) Multiple choice questions
1. A dependent variable is also known as a ___.
a. explanatory variable
b. control variable
c. predictor variable
d. response variable
2. In the equation y = β0 + β1x + u, β0 is the __
a. dependent variable
b. independent variable
c. slope parameter
d. intercept parameter.
3. What does the equation ŷ = β0
̂ + β1
̂x denote if the regression equation is y = β0 + β1x1 + u?
a. The explained sum of squares
b. The total sum of squares
c. The sample regression function
d. The population regression function
4. If the total sum of squares (SST) in a regression equation is 81, and the residual sum of
squares (SSR) is 25, what is the explained sum of squares (SSE)?
a. 64
b. 56
c. 32
d. 18
5. If the residual sum of squares (SSR) in a regression analysis is 66 and the total sum of
squares (SST) is equal to 90, what is the value of the R-squared?
a. 0.73
b. 0.55
c. 0.27
d. 1.2
Econometrics Ketevani Kapanadze
6. The error term in a regression equation is said to exhibit homoskedasticty if _____.
a. it has zero conditional mean
b. it has the same variance for all values of the explanatory variable.
c. it has the same value for all values of the explanatory variable
d. if the error term has a value of one given any value of the explanatory variable.
7. In the equation, y = β0 + β1x1 + β2x2 + u, β2 is a(n) _____.
a. independent variable
b. dependent variable
c. slope parameter
d. intercept parameter
8. Consider the following regression equation: y = β1
+ β2
x1 + β2
x2 + u. What does β1
imply?
a.β1 measures the ceteris paribus effect of x1on x2.
b. β1 measures the ceteris paribus effect of y on x1.
c. β1 measures the ceteris paribus effect of x1on y.
d. β1 measures the ceteris paribus effect of x1on u.
9. High (but not perfect) correlation between two or more independent variables is called
_____.
a. heteroskedasticty
b. homoskedasticty
c. multicollinearity
d. micronumerosity
10. The normality assumption implies that:
a. the population error u is dependent on the explanatory variables and is normally distributed
with mean equal to one and variance σ2.
b. the population error u is independent of the explanatory variables and is normally
distributed with mean equal to one and variance σ.
Econometrics Ketevani Kapanadze
c. the population error u is dependent on the explanatory variables and is normally distributed
with mean zero and variance σ.
d. the population error u is independent of the explanatory variables and is normally
distributed with mean zero and variance σ2.
11. Which of the following is a statistic that can be used to test hypotheses about a single
population parameter?
a. F statistic
b. t statistic
c. χ2 statistic
d. Durbin-Watson statistic
12. Consider the equation, Y = β1 + β2X2 + u. A null hypothesis, H0: β2 = 0 states that:
a. X2 has no effect on the expected value of β2.
b. X2 has no effect on the expected value of Y.
c. β2 has no effect on the expected value of Y.
d. Y has no effect on the expected value of X2.
13. The significance level of a test is:
a. the probability of rejecting the null hypothesiswhen it is false.
b. one minus the probability of rejecting the null hypothesis when it is false.
c. the probability of rejecting the null hypothesis when it is true.
d. one minus the probability of rejecting the null hypothesis when it is true.
14. Which of the following tools is used to test multiple linear restrictions?
a. t test
b. z test
c. F test
d. Unit root test
15. Which of the following is true of heteroskedasticity?
a. Heteroskedasticty causes inconsistency in the Ordinary Least Squares estimators.
Econometrics Ketevani Kapanadze
b. Population R2 is affected by the presence of heteroskedasticty.
c. The Ordinary Least Square estimators are not the best linear unbiased estimators if
heteroskedasticity is present.
d. It is not possible to obtain F statistics that are robust to heteroskedasticity of an unknown
form.
16. Which of the following is true of the OLS t statistics?
a. The heteroskedasticity-robust t statistics are justified only if the sample size is large.
b. The heteroskedasticty-robust t statistics are justified only if the sample size is small.
c. The usual t statistics do not have exact t distributions if the sample size is large.
d. In the presence of homoskedasticity, the usual t statistics do not have exact t distributions if
the sample size is small.
17. Which of the following tests helps in the detection of heteroskedasticity?
a. The Breusch-Pagan test
b. The Breusch-Godfrey test
c. The Durbin-Watson test
d. The Chow test
18. A test for heteroskedasticty can be significant if _____.
a. the Breusch-Pagan test results in a large p-value
b. the White test results in a large p-value
c. the functional form of the regression model is misspecified
d. the regression model includes too many independent variables
19. Which of the following is true of the White test?
a. The White test is used to detect the presence of multicollinearity in a linear regression
model.
b. The White test cannot detect forms of heteroskedasticity that invalidate the usual Ordinary
Least Squares standard errors.
c. The White test can detect the presence of heteroskedasticty in a linear regression model
even if the functional form is misspecified.
d. The White test assumes that the square of the error term in a regression model is
uncorrelated with all the independent variables, their squares and cross products.
Econometrics Ketevani Kapanadze
20. Consider the following simple regression model: y = β0 + β1x1 + u. Suppose z is an
instrument for x. Which of the following conditions denotes instrument exogeneity?
a. Cov(z,u) > 0
b. Cov(z,x) > 0
c. Cov(z,u) = 0
d. Cov(z,x) = 0
21. Consider the following simple regression model y=β0 + β1x1 + u. Suppose z is an
instrument for x. Which of the following statements is true?
a. The condition Cov(z,u) = 0 can be tested statistically.
b. The condition Cov(z,x) ≠ 0 cannot be tested statistically.
c. The ordinary least squares estimator is always biased if Cov(x,u)≠0.
d. The ordinary least squares estimator is unbiased if Cov(x,u)≠0.
22. Consider the following simple regression model y=β0 + β1x1 + u. The variable z is a poor
instrument for x if _____.
a. there is a high correlation between z and x
b. there is a low correlation between z and x
c. there is a high correlation between z and u
d. there is a low correlation between z and u
23. Which of the following assumptions is known as exclusion restrictions?
a. The assumption that an instrumental variable is excluded from a regression model and is
correlated with the error term
b. The assumption that an instrumental variable is excluded from a regression model and
correlated with an exogenous explanatory variable
c. The assumption that an exogenous explanatory variable is excluded from a regression model
and is uncorrelated with the error term
d. The assumption that an endogenous explanatory variable excluded from a regression model
and is uncorrelated with the error term
Econometrics Ketevani Kapanadze
24. In the equation c = β0 + β1i + u, c denotes consumption and i denotes income. What is the
residual for the 5th observation if c5=$500 and c5̂ =$475?
a. $975
b. $300
c. $25
d. $50
25. In a regression model, which of the following will be described using a binary variable?
a. Whether it rained on a particular day or it did not
b. The volume of rainfall during a year
c. The percentage of humidity in air on a particular day
d. The concentration of dust particles in air
26. The binary dependent variable model is an example of a
a. regression model, which has as a regressor, among others, a binary variable.
b. model that cannot be estimated by OLS.
c. limited dependent variable model.
d. model where the left-hand variable is measured in base 2
27. In the linear probability model, the interpretation of the slope coefficient is
a. the change in odds associated with a unit change in X, holding other regressors constant.
b. not all that meaningful since the dependent variable is either 0 or 1.
c. the change in probability that Y=1 associated with a unit change in X, holding others
regressors constant.
d. the response in the dependent variable to a percentage change in the regressor.
Econometrics Ketevani Kapanadze
b) Conceptual questions
1) Explain what does unbiasedness means.
2) Explain what does exogenous and endogenous variable means.
3) Define and explain the concept of R-squared.
4) Explain what happens when we omit important variable from the model.
5) Explain the concept of the confidence intervals.
6) Describe the heteroskedasticity problem: explain briefly, what it is and how it affects the
estimation.
7) Name and discuss the steps of one of the tests for heteroscedasticity and discuss its
flows.
8) Describe Linear Probability Model and state its advantages and disadvantages.
9) Explain the concept of an instrumental variable.
10) Describe the properties that valid instrumental variable should satisfy.
c) True/False questions
1. The ideal way to analyze causation is to use experimental data.
2. The variance of the slope estimator increases as the error variance decreases.
3. If the calculated value of the t-statistic is greater than the critical value, the null
hypothesis, H0 is rejected in favor of the alternative hypothesis, H1.
4. One advantage of the Linear Probability Model is that it is easy to estimate and to
interpret.
5. Under the Gauss-Markov assumptions, OLS estimators are BLUE.
6. Sum of squared residuals (SSR) is greater in the unrestricted model.
7. For estimating population parameters more precisely one would prefer to have low
variation in explanatory variables and high variation in error term.
8. In the Linear Probability Model (LPM) predicted values are always between 0 and 1.
Econometrics Ketevani Kapanadze
9. The dummy variable coefficient for a particular group represents the estimated difference in
intercepts between that group and the base group.
10. If the heteroskedasticity is present in the model, than estimates are no longer unbiased.
d) Solve the problem
Consider equation relating education, experience and race of the person to her wage in the
following manner:
ln(𝑤𝑎𝑔𝑒) = 𝛽0 + 𝛽1 ∗ 𝑒𝑑𝑢𝑐 + 𝛽2 ∗ 𝑒𝑥𝑝𝑒𝑟 + 𝛽3 ∗ 𝑒𝑥𝑝𝑒𝑟2
+ 𝛽4 ∗ 𝑏𝑙𝑎𝑐𝑘 + 𝑢
where the variables are defined as follows:
wage Wage of a person in USD
educ Number of years of education
exper Work experience in years
black 1 if the person is black, 0 otherwise
a) Explain what signs you expect for each of the parameters.
b) Suppose the equation is estimated using a random sample of 935 workers. Argue whether
all of the Classical Linear Model assumptions will be satisfied.
c) The estimated output of the equation is presented below. Interpret all the coefficients.
Do they have expected signs? What percentage of variation in wages do we explain using
our controls?
d) According to the output, what factors are important determinants of wage?
e) Test the overall significance of the regression: explicitly state the null and alternative
hypothesis and the result of the test.
Econometrics Ketevani Kapanadze
f) Suppose you want to test the hypothesis that returns to education is lower for black
people. How would you test it?
Model 1: OLS, using observations 1-935
Dependent variable: l_wage
Coefficient Std. Error t-ratio p-value
const 5.64834 0.124761 45.2733 XXXXX
educ 0.0714961 0.00660733 10.8207 XXXXX
exper 0.0139896 0.0133153 1.0506 XXXXX
sq_exper 0.000225854 0.000557475 0.4051 XXXXX
black −0.222567 0.0384461 −5.7891 XXXXX
Mean dependent var 6.779004 S.D. dependent var 0.421144
Sum squared resid 138.9600 S.E. of regression 0.386548
R-squared 0.161155 Adjusted R-squared 0.157547
F(4, 930) 44.66678 P-value(F) 2.47e-34
Log-likelihood −435.4839 Akaike criterion 880.9679
Schwarz criterion 905.1706 Hannan-Quinn 890.1966