Introductory Statistics for Economists
Question Bank
Course Introduction
Introductory Statistics for Economists provides students with a foundational understanding of statistical concepts and methods as they apply to economics. The course covers topics such as descriptive statistics, probability theory, random variables, sampling distributions, estimation, hypothesis testing, and regression analysis. Emphasis is placed on interpreting and analyzing economic data, drawing inferences, and applying statistical reasoning to real-world economic problems. Through lectures, examples, and practical exercises, students develop quantitative skills essential for further study and research in economics.
Recommended Textbook
Introduction to Econometrics Update 3rd Edition by James H. Stock
Available Study Resources on Quizplus
18 Chapters
982 Verified Questions
982 Flashcards
Source URL: https://quizplus.com/study-set/3376
Page 2
Chapter 1: Economic Questions and Data
Available Study Resources on Quizplus for this Chatper
17 Verified Questions
17 Flashcards
Source URL: https://quizplus.com/quiz/66988
Sample Questions
Q1) Give at least three examples from economics where each of the following type of data can be used: cross-sectional data, time series data, and panel data.
Answer: Answers will vary by student. At this level of economics, students most likely have heard of the following use of cross-sectional data: earnings functions, growth equations, the effect of class size reduction on student performance (in this chapter), demand functions (in this chapter: cigarette consumption); time series: the Phillips curve (in this chapter), consumption functions, Okun's law; panel data: various U.S. state panel studies on road fatalities (in this book), unemployment rate and unemployment benefits variations, growth regressions (across states and countries), and crime and abortion (Freakonomics).
Q2) The reason why economists do not use experimental data more frequently is for all of the following reasons except that real-world experiments
A)cannot be executed in economics.
B)with humans are difficult to administer.
C)are often unethical.
D)have flaws relative to ideal randomized controlled experiments.
Answer: A
To view all questions and flashcards with answers, click on the resource link above.
Page 3
Chapter 2: Review of Probability
Available Study Resources on Quizplus for this Chatper
70 Verified Questions
70 Flashcards
Source URL: https://quizplus.com/quiz/66989
Sample Questions
Q1) Show that the correlation coefficient between Y and X is unaffected if you use a linear transformation in both variables. That is, show that corr(X,Y)= corr(X<sup>*</sup>, Y<sup>*</sup>), where X<sup>*</sup> = a + bX and Y<sup>*</sup> = c + dY, and where a, b, c, and d are arbitrary non-zero constants. Answer: corr(X<sup>*</sup>, Y<sup>*</sup>)= \[\frac { \operatorname { cov } \left( X ^ { * } , Y ^ { * } \right) } { \sqrt { \operatorname { var } ( X ^ { * } ) \sqrt { \operatorname { var } ( Y^ { * } ) } } } = \frac { b d \operatorname { cov } ( X , Y ) } { \sqrt { b ^ { 2 } \operatorname { var } ( X ) \sqrt { d ^ { 2 } \operatorname { var } ( Y ) } } }\] corr(X, Y).
Q2) Assume that Y is normally distributed N(?, ?<sup>2</sup>). To find Pr(c<sub>1</sub> ? Y ? c<sub>2</sub>), where c<sub>1</sub> < c<sub>2</sub> and d<sub>i</sub> = \(\frac { c _ { 1 } - \mu } { \sigma }\) , you need to calculate Pr(d<sub>1</sub> ? Z ? d<sub>2</sub>)=
A)?(d<sub>2</sub>)- ?(d<sub>1</sub>)
B)?(1.96)- ?(1.96)
C)?(d<sub>2</sub>)- (1 - ?(d<sub>1</sub>))
D)1 - (?(d<sub>2</sub>)- ?(d<sub>1</sub>))
Answer: A
To view all questions and flashcards with answers, click on the resource link above.
Page 4
Chapter 3: Review of Statistics
Available Study Resources on Quizplus for this Chatper
65 Verified Questions
65 Flashcards
Source URL: https://quizplus.com/quiz/66990
Sample Questions
Q1) A low correlation coefficient implies that A)the line always has a flat slope
B)in the scatterplot, the points fall quite far away from the line C)the two variables are unrelated D)you should use a tighter scale of the vertical and horizontal axis to bring the observations closer to the line
Answer: B
Q2) If the null hypothesis states H<sub>0</sub> : E(Y)= µ<sub>Y,0</sub>, then a two-sided alternative hypothesis is
A)H<sub>1</sub> : E(Y)? µ<sub>Y,0</sub>.
B)H<sub>1</sub> : E(Y)? µ<sub>Y,0</sub>.
C)H<sub>1</sub> : \( { \mu }_Y\) < µ<sub>Y,0</sub>.
D)H<sub>1</sub> : E(Y)> µ<sub>Y,0</sub>.
Answer: A
To view all questions and flashcards with answers, click on the resource link above.
Page 5
Chapter 4: Linear Regression With One Regressor
Available Study Resources on Quizplus for this Chatper
65 Verified Questions
65 Flashcards
Source URL: https://quizplus.com/quiz/66991
Sample Questions
Q1) You have obtained a sample of 14,925 individuals from the Current Population Survey (CPS)and are interested in the relationship between average hourly earnings and years of education. The regression yields the following result: \(\hat { a h e }\) = -4.58 + 1.71×educ , R<sup>2</sup><sup> </sup>= 0.182, SER = 9.30 where ahe and educ are measured in dollars and years respectively.
a. Interpret the coefficients and the regression R<sup>2</sup>.
b. Is the effect of education on earnings large?
c. Why should education matter in the determination of earnings? Do the results suggest that there is a guarantee for average hourly earnings to rise for everyone as they receive an additional year of education? Do you think that the relationship between education and average hourly earnings is linear?
d. The average years of education in this sample is 13.5 years. What is mean of average hourly earnings in the sample?
e. Interpret the measure SER. What is its unit of measurement.
Q2) In order to calculate the slope, the intercept, and the regression R<sup>2</sup> for a simple sample regression function, list the five sums of data that you need.
To view all questions and flashcards with answers, click on the resource link above.
6
Chapter 5: Regression With a Single Regressor: Hypothesis
Tests and Confidence Intervals
Available Study Resources on Quizplus for this Chatper
59 Verified Questions
59 Flashcards
Source URL: https://quizplus.com/quiz/66992
Sample Questions
Q1) Using the textbook example of 420 California school districts and the regression of testscores on the student-teacher ratio, you find that the standard error on the slope coefficient is 0.51 when using the heteroskedasticity robust formula, while it is 0.48 when employing the homoskedasticity only formula. When calculating the t-statistic, the recommended procedure is to
A)use the homoskedasticity only formula because the t-statistic becomes larger B)first test for homoskedasticity of the errors and then make a decision
C)use the heteroskedasticity robust formula
D)make a decision depending on how much different the estimate of the slope is under the two procedures
Q2) Heteroskedasticity means that
A)homogeneity cannot be assumed automatically for the model.
B)the variance of the error term is not constant.
C)the observed units have different preferences.
D)agents are not all rational.
Q3) Explain carefully the relationship between a confidence interval, a one-sided hypothesis test, and a two-sided hypothesis test. What is the unit of measurement of the t-statistic?
To view all questions and flashcards with answers, click on the resource link above. Page 7
Chapter 6: Linear Regression With Multiple Regressors
Available Study Resources on Quizplus for this Chatper
65 Verified Questions
65 Flashcards
Source URL: https://quizplus.com/quiz/66993
Sample Questions
Q1) The sample regression line estimated by OLS
A)has an intercept that is equal to zero.
B)is the same as the population regression line.
C)cannot have negative and positive slopes.
D)is the line that minimizes the sum of squared prediction mistakes.
Q2) Imagine you regressed earnings of individuals on a constant, a binary variable ("Male")which takes on the value 1 for males and is 0 otherwise, and another binary variable ("Female")which takes on the value 1 for females and is 0 otherwise. Because females typically earn less than males, you would expect
A)the coefficient for Male to have a positive sign, and for Female a negative sign.
B)both coefficients to be the same distance from the constant, one above and the other below.
C)none of the OLS estimators to exist because there is perfect multicollinearity.
D)this to yield a difference in means statistic.
Q3) (Requires Calculus)For the case of the multiple regression problem with two explanatory variables, derive the OLS estimator for the intercept and the two slopes.
To view all questions and flashcards with answers, click on the resource link above. Page 8
Chapter 7: Hypothesis Tests and Confidence Intervals in Multiple
Regression
Available Study Resources on Quizplus for this Chatper
64 Verified Questions
64 Flashcards
Source URL: https://quizplus.com/quiz/66994
Sample Questions
Q1) The homoskedasticity-only F-statistic and the heteroskedasticity-robust F-statistic typically are
A)the same
B)different
C)related by a linear function
D)a multiple of each other (the heteroskedasticity-robust F-statistic is 1.96 times the homoskedasticity-only F-statistic)
Q2) The overall regression F-statistic tests the null hypothesis that
A)all slope coefficients are zero.
B)all slope coefficients and the intercept are zero.
C)the intercept in the regression and at least one, but not all, of the slope coefficients is zero.
D)the slope coefficient of the variable of interest is zero, but that the other slope coefficients are not.
Q3) For a single restriction (q = 1), the F-statistic
A)is the square root of the t-statistic.
B)has a critical value of 1.96.
C)will be negative.
D)is the square of the t-statistic.
Page 9
To view all questions and flashcards with answers, click on the resource link above.
Chapter 8: Nonlinear Regression Functions
Available Study Resources on Quizplus for this Chatper
63 Verified Questions
63 Flashcards
Source URL: https://quizplus.com/quiz/66995
Sample Questions
Q1) In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
A) Y = f(X<sub>1</sub> + X<sub>1</sub>, X<sub>2</sub>,... X<sub>k</sub>).
B) Y = f(X<sub>1</sub> + X<sub>1</sub>, X<sub>2</sub> + X<sub>2</sub>,..., X<sub>k</sub>+ X<sub>k</sub>)- f(X<sub>1</sub>, X<sub>2</sub>,...X<sub>k</sub>).
C) Y = f(X<sub>1</sub> + X<sub>1</sub>, X<sub>2</sub>,..., X<sub>k</sub>)f(X<sub>1</sub>, X<sub>2</sub>,...X<sub>k</sub>).
D) Y = f(X<sub>1</sub> + X<sub>1</sub>, X<sub>2</sub>,..., X<sub>k</sub>)f(X<sub>1</sub>, X<sub>2</sub>,...X<sub>k</sub>).
Q2) In the case of perfect multicollinearity, OLS is unable to estimate the slope coefficients of the variables involved. Assume that you have included both X<sub>1</sub> and X<sub>2</sub> as explanatory variables, and that X<sub>2</sub> = X \(\begin{array} { l } 2 \\
1 \end{array}\) , so that there is an exact relationship between two explanatory variables. Does this pose a problem for estimation?
To view all questions and flashcards with answers, click on the resource link above. Page 10
Chapter 9: Assessing Studies Based on Multiple Regression
Available Study Resources on Quizplus for this Chatper
65 Verified Questions
65 Flashcards
Source URL: https://quizplus.com/quiz/66996
Sample Questions
Q1) Your textbook has analyzed simultaneous equation systems in the case of two equations, Y<sub>i</sub> = <sub>0</sub> + <sub>1</sub>X<sub>i</sub> + u<sub>i</sub> <sub> </sub>X<sub>i</sub> = \(\gamma _ { 0 }\) + \(\gamma _ { 1 }\) Y<sub>i</sub> + v<sub>i</sub>, where the first equation might be the labor demand equation (with capital stock and technology being held constant), and the second the labor supply equation (X being the real wage, and the labor market clears). What if you had a a production function as the third equation Z<sub>i</sub> = \(\delta _ { 0 }\) + \(\delta _ { 1 }\) Y<sub>i</sub> + w<sub>i</sub> where Z is output. If the error terms, u, v, and w, were pairwise uncorrelated, explain why there would be no simultaneous causality bias when estimating the production function using OLS.
Q2) Think of three different economic examples where cross-sectional data could be collected. Indicate in each of these cases how you would check if the analysis is externally valid.
To view all questions and flashcards with answers, click on the resource link above.
11
Chapter 10: Regression With Panel Data
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/66997
Sample Questions
Q1) The main advantage of using panel data over cross sectional data is that it
A)gives you more observations.
B)allows you to analyze behavior across time but not across entities.
C)allows you to control for some types of omitted variables without actually observing them.
D)allows you to look up critical values in the standard normal distribution.
Q2) It is advisable to use clustered standard errors in panel regressions because
A)without clustered standard errors, the OLS estimator is biased
B)hypothesis testing can proceed in a standard way even if there are few entities (n is small)
C)they are easier to calculate than homoskedasticity-only standard errors
D)the fixed effects estimator is asymptotically normally distributed when n is large
Q3) Time Fixed Effects regression are useful in dealing with omitted variables
A)even if you only have a cross-section of data available.
B)if these omitted variables are constant across entities but vary over time.
C)when there are more than 100 observations.
D)if these omitted variables are constant across entities but not over time.
To view all questions and flashcards with answers, click on the resource link above.
Page 12
Chapter 11: Regression With a Binary Dependent Variable
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/66998
Sample Questions
Q1) Nonlinear least squares
A)solves the minimization of the sum of squared predictive mistakes through sophisticated mathematical routines, essentially by trial and error methods. B)should always be used when you have nonlinear equations.
C)gives you the same results as maximum likelihood estimation.
D)is another name for sophisticated least squares.
Q2) Sketch the regression line for the linear probability model with a single regressor. Indicate for which values of the slope and intercept the predictions will be above one and below zero. Can you rule out homoskedasticity in the error terms with certainty here?
Q3) Probit coefficients are typically estimated using A)the OLS method
B)the method of maximum likelihood
C)non-linear least squares (NLLS)
D)by transforming the estimates from the linear probability model
Q4) (Requires Appendix material)Briefly describe the difference between the following models: censored and truncated regression model, count data, ordered responses, and discrete choice data. Try to be specific in terms of describing the data involved.
To view all questions and flashcards with answers, click on the resource link above.
Page 13
Chapter 12: Instrumental Variables Regression
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/66999
Sample Questions
Q1) (Requires Chapter 8)When using panel data and in the presence of endogenous regressors
A)the TSLS does not exist.
B)you do not have to worry about the validity of instruments, since there are so many fixed effects.
C)the OLS estimator is consistent.
D)application of the TSLS estimator is straightforward if you use two time periods and difference the data.
Q2) In the case of the simple regression model Y<sub>i</sub> = <sub>0</sub> + <sub>1</sub>X<sub>i</sub> + u<sub>i</sub>, i = 1, , n, when X and u are correlated, then
A)the OLS estimator is biased in small samples only.
B)OLS and TSLS produce the same estimate.
C)X is exogenous.
D)the OLS estimator is inconsistent.
Q3) Endogenous variables
A)are correlated with the error term.
B)always appear on the LHS of regression functions.
C)cannot be regressors.
D)are uncorrelated with the error term.
To view all questions and flashcards with answers, click on the resource link above.
Page 14
Chapter 13: Experiments and Quasi-Experiments
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/67000
Sample Questions
Q1) Heterogeneous population
A)implies that heteroskedasticity-robust standard errors must be used.
B)suggest that multiple characteristics must be used to describe the population.
C)effects can be captured through interaction terms.
D)refers to circumstances in which there is unobserved variation in the causal effect with the population.
Q2) A repeated cross-sectional data set is
A)a collection of cross-sectional data sets, where each cross-sectional data set corresponds to a different time period.
B)the same as a balanced panel data set.
C)what Card and Krueger used in their study of the effect of minimum wages on teenage employment.
D)time series.
Q3) The following does not represent a threat to internal validity of randomized controlled experiments:
A)attrition.
B)failure to follow the treatment protocol.
C)experimental effects.
D)a large sample size.
To view all questions and flashcards with answers, click on the resource link above.
Page 15
Chapter 14: Introduction to Time Series Regression and Forecasting
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/67001
Sample Questions
Q1) You should use the QLR test for breaks in the regression coefficients, when A)the Chow F-test has a p value of between 0.05 and 0.10.
B)the suspected break data is not known.
C)there are breaks in only some, but not all, of the regression coefficients. D)the suspected break data is known.
Q2) You have collected data for real GDP (Y)and have estimated the following function: ln \(\hat { Y }\) <sub>t</sub> = 7.866 + 0.00679×Zeit
(0.007)(0.00008)
t = 1961:I - 2007:IV, R<sup>2</sup> = 0.98, SER = 0.036
where Zeit is a deterministic time trend, which takes on the value of 1 during the first quarter of 1961, and is increased by one for each following quarter.
a. Interpret the slope coefficient. Does it make sense?
b. Interpret the regression R<sup>2</sup>. Are you impressed by its value?
c. Do you think that given the regression R<sup>2</sup>, you should use the equation to forecast real GDP beyond the sample period?
To view all questions and flashcards with answers, click on the resource link above.
Page 16
Chapter 15: Estimation of Dynamic Causal Effects
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/67002
Sample Questions
Q1) Consider the distributed lag model Y<sub>t</sub> = <sub>0</sub> + <sub>1</sub>X<sub>t</sub> + <sub>2</sub>X<sub>t</sub><sub>-</sub><sub>1</sub> + <sub>3</sub>X<sub>t</sub><sub>-</sub><sub>2</sub> + + <sub>r</sub><sub>+</sub><sub>1</sub>X<sub>t</sub><sub>-</sub><sub>r</sub> + u<sub>t. </sub>The dynamic causal effect is
A) <sub>0</sub> + <sub>1</sub>
B) <sub>1</sub> + <sub>2</sub>+ + <sub>r</sub><sub>+</sub><sub>1</sub>
C) <sub>0</sub> + <sub>1</sub>+ + <sub>r</sub><sub>+</sub><sub>1</sub>
D) <sub>1</sub>
Q2) Ascertaining whether or not a regressor is strictly exogenous or exogenous ultimately requires all of the following with the exception of A)economic theory.
B)institutional knowledge.
C)expert judgment.
D)use of HAC standard errors.
Q3) The Cochrane-Orcutt iterative method is
A)a special case of GLS estimation.
B)a method to compute HAC standard errors.
C)a special case of maximum likelihood estimation.
D)a grid search for the autoregressive parameters on the error process.
To view all questions and flashcards with answers, click on the resource link above. Page 17
Chapter 16: Additional Topics in Time Series Regression
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/67003
Sample Questions
Q1) The coefficients of the VAR are estimated by A)using a simultaneous estimation method such as TSLS.
B)maximum likelihood.
C)panel methods.
D)estimating each of the equations by OLS.
Q2) In a VECM,
A)past values of Y<sub>t</sub> - X<sub>t</sub> help to predict future values of Y<sub>t</sub> and/or X<sub>t</sub>.
B)errors are corrected for serial correlation using the Cochrane-Orcutt method.
C)current values of Y<sub>t</sub> - X<sub>t</sub> help to predict future values of Y<sub>t</sub> and/or X<sub>t</sub>.
D)VAR techniques, such as information criteria, no longer apply.
Q3) Under the VAR assumptions, the OLS estimators are
A)consistent and have a joint normal distribution even in small samples. B)BLUE.
C)consistent and have a joint normal distribution in large samples. D)unbiased.
To view all questions and flashcards with answers, click on the resource link above.
Page 18
Chapter 17: The Theory of Linear Regression With One Regressor
Available Study Resources on Quizplus for this Chatper
49 Verified Questions
49 Flashcards
Source URL: https://quizplus.com/quiz/67004
Sample Questions
Q1) Your textbook states that an implication of the Gauss-Markov theorem is that the sample average, \(\bar { Y }\) , is the most efficient linear estimator of E(Y<sub>i</sub>)when Y<sub>1</sub>,..., Y<sub>n</sub> are i.i.d. with E(Y<sub>i</sub>)= <sub>Y</sub> and var(Y<sub>i</sub>)= \(\sigma \stackrel { 2 } { Y }\) This follows from the regression model with no slope and the fact that the OLS estimator is BLUE. Provide a proof by assuming a linear estimator in the Y's, \(\tilde { \mu } = \sum _ { i = 1 } ^ { n } a _ { i } Y _ { i }\) (a)State the condition under which this estimator is unbiased. (b)Derive the variance of this estimator.
(c)Minimize this variance subject to the constraint (condition)derived in (a)and show that the sample mean is BLUE.
Q2) You need to adjust \(S _ {\hat{ u }} ^ { 2 }\) by the degrees of freedom to ensure that \(S _ {\hat{ u }} ^ { 2 }\) is
A)an unbiased estimator of \(\sigma _ { u } ^ { 2 }\)
B)a consistent estimator of \(\sigma _ { u } ^ { 2 }\)
C)efficient in small samples.
D)F-distributed.
Q3) (Requires Appendix material)State and prove the Cauchy-Schwarz Inequality.
To view all questions and flashcards with answers, click on the resource link above.
Page 19
Chapter 18: The Theory of Multiple Regression
Available Study Resources on Quizplus for this Chatper
50 Verified Questions
50 Flashcards
Source URL: https://quizplus.com/quiz/67005
Sample Questions
Q1) The difference between the central limit theorems for a scalar and vector-valued random variables is
A)that n approaches infinity in the central limit theorem for scalars only.
B)the conditions on the variances.
C)that single random variables can have an expected value but vectors cannot. D)the homoskedasticity assumption in the former but not the latter.
Q2) The OLS estimator
A)has the multivariate normal asymptotic distribution in large samples. B)is t-distributed.
C)has the multivariate normal distribution regardless of the sample size. D)is F-distributed.
Q3) \(\hat \beta\) - ?
A)cannot be calculated since the population parameter is unknown.
B)= ( \(X ^ { \prime }\) X)<sup>-</sup><sup>1</sup> <sup> </sup> \(X ^ { \prime }\) <sup>U</sup>.
C)= Y - \(\hat { Y }\)
D)= ? + ( \(X ^ { \prime }\) X)<sup>-</sup><sup>1</sup> <sup> </sup> \(X ^ { \prime }\) <sup>U</sup>
Q4) Write an essay on the difference between the OLS estimator and the GLS estimator.
To view all questions and flashcards with answers, click on the resource link above. Page 20