Econometric Methods
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Course Introduction
Econometric Methods introduces students to the fundamental concepts and techniques used to analyze economic data. The course covers topics such as statistical inference, regression analysis, hypothesis testing, and model specification, with a focus on the classical linear regression model. Students will learn to estimate and interpret economic relationships, diagnose model issues, and apply econometric software to real-world datasets. Emphasis is placed on understanding the assumptions underlying econometric models and how violations of these assumptions can impact empirical results, preparing students for applied research in economics and related fields.
Recommended Textbook
Practical Econometrics data collection analysis and application 1st Edition by Christiana E. Hilmer
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2
Chapter 1: An Introduction to Econometrics and Statistical
Inference
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Sample Questions
Q1) A statistic is
A)a function that is computed from the sample data.
B)a function that exists within the population.
C)the true population parameter.
D)constant.
Answer: A
Q2) What is a sampling distribution? How do you construct one? Why is it important to understand what a sampling distribution is? Explain.
Answer: A sampling distribution is the distribution of a sample statistic,such as the sample mean.It is constructed by drawing every possible sample of size n from the population of size N,calculating the value of a sample statistic for each sample,and placing all of those calculated values in order on a number line.It is important to understand this definition because statistics and hypothesis testing is based on principles learned from our knowledge of what sampling distributions look like.
Q3) What is a statistic? A parameter? How are the two related? Explain.
Answer: A statistic is a function that is computed from the sample data.A parameter is a function that exists within the population.A sample statistic serves as a point estimate of the likely value of an unobserved parameter.
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Chapter 2: Collection and Management of Data
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Sample Questions
Q1) Cross-sectional data is data collected
A)for a number of individuals,countries,firms,etc.over many different time periods.
B)for a given individual,country,firm,etc.over many different time periods.
C)for many different individuals,countries,firms,etc.in a given time-period.
D)with replacement.
Answer: B
Q2) Why do we recommend saving one master file while performing calculations in another file? Explain.
Answer: We recommend saving one master file so that if we make a mistake and overwrite or otherwise change our data,we can easily go back and reconstruct our correct data without having to start at square one with our internet search,data downloading,and so on.
Q3) Why do we suggest making file and variable names as intuitive as possible? Explain.
Answer: We recommend making file and variable names as intuitive as possible because we are often forced to put our project aside for longer periods of time and we need to be able to get back up-to-speed as quickly as possible when returning to it.If our file and variable names are not intuitive,then doing so is much more difficult and time-consuming.
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4
Chapter 3: Summary Statistics
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Sample Questions
Q1) a.If the correlation coefficient between two random variables equals zero,does that imply that there is no relationship between those random variables?
b.If the correlation coefficient between two random variables is close to one in absolute value,does that imply that one random variable causes another random variable?
Answer: a.No,the correlation coefficient only measures if there is a linear relationship between the two random variables.It could be that there is no relationship between the two variables but it could also be that the two variables are related to each other in some non-linear way.
b.A high correlation coefficient does not imply that one variable causes another variable.It could be that there is spurious correlation between the two variables in that they are related to a third random variable.
Q2) The correlation coefficient is
A)must be positive.
B)the square root of the covariance.
C)must be negative.
D)must fall between -1 and 1.
Answer: D
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Page 5
Chapter 4: Simple Linear Regression
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Sample Questions
Q1) In general,a larger \(s _ { y \mid x }\)
Tends to suggest that
A)the estimated sample regression function explains a greater percentage of the total variation in y.
B)the estimated sample regression function is more accurate.
C)the data points fall closer to the best-fit line.
D)the data points fall further from the best-fit line.
Q2) The residual is
A)the vertical distance between the observed value of y and the mean value of y.
B)the vertical distance between the predicted value of y and the mean value of y.
C)the vertical distance between the observed value of y and the probabilistic value of y.
D)the vertical distance between the observed value of y and the predicted value of y.
Q3) The estimated intercept
A)is the estimated marginal effect of x on y.
B)is the estimated value of y when x equals 0.
C)is equal to the population intercept.
D)is \(\hat { \beta } _ { 1 }\) .
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Chapter 5: Hypothesis Testing in Linear Regression Analysis
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Sample Questions
Q1) Based on the Excel output in Figure 5.2,you should conclude that a
A)one percentage point increase in the percentage of adults with a Bachelor's degree is associated with a statistically insignificant 40.59 percent increase in the obesity rate,holding all else constant.
B)one percentage point increase in the percentage of adults with a Bachelor's degree is associated with a statistically significant 40.59 percent increase in the obesity rate,holding all else constant.
C)one percentage point increase in the percentage of adults with a Bachelor's degree is associated with a statistically insignificant .466 percentage point increase in the obesity rate,holding all else constant.
D)one percentage point increase in the percentage of adults with a Bachelor's degree is associated with a statistically significant .466 percentage point increase in the obesity rate,holding all else constant.
Q2) An estimator is efficient if it
A)has the smallest variance of all unbiased estimators.
B)has a p-value is less than .05.
C)has a small standard error.
D)has the smallest mean squared error.
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Page 7
Chapter 6: Multiple Linear Regression Analysis
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Sample Questions
Q1) The test statistic for this Chow test is A) \( \frac{USSpooled / k+1}{\left(U S S_{4}+U S S_{2}\right) / n-2(k+1)} \)
B) \(\frac { \text { USS } _ { 1 } + \text { USS } _ { 2 } / k + 1 } { \text { (USS } \left. _ { 1 } + \text { USS } _ { 2 } \right) / n - 2 ( k + 1 ) }\)
C) \(\frac { \left( \text { USS } _ { p o o l e d } - \left( \text { USS } _ { 1 } + \text { USS } _ { 2 } \right) \right) / k + 1 } { \left( U S S _ { 1 } + \text { USS } _ { 2 } \right) / ( k + 1 ) }\)
D) \(\frac { \left( \text { USS } _ { p o o l e d } - \left( \text { USS } _ { 1 } + U S S _ { 2 } \right) \right) / k + 1 } { \left( U S S _ { 1 } + U S S _ { 2 } \right) / n - 2 ( k + 1 ) }\)
Q2) Why is the "all other independent variables constant" condition important? Explain.
Q3) How do you perform a test of the individual significance of a slope coefficient? What are the null and alternative hypothesis for this test? What is the rejection rule? What is the intuition for why the test works? Explain.
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Chapter 7: Qualitative Variables and Non-Linearities in
Multiple Linear Regression Analysis
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Sample Questions
Q1) Suppose you estimate the sample regression function \[\begin{array} { l } viol\widehat {ent~c}rime _ { i } = 7.23 - 4.87 \cdot \text { Suburb } _ { i } + 6.11 \cdot \text { Unemployment } _ { i } \\ - 1.30 \cdot ( \text { Suburb* Unemployment } ) _ { i } \\ \end{array}\]
You should conclude that the marginal effect of unemployment on violent crime is A)the same in cities and suburbs.
B)higher in cities than in suburbs.
C)lower in cities than in suburbs.
D)possibly different in cities and suburbs but we cannot tell from this regression.
Q2) Quadratic terms allow the estimated
A)slope to differ for different values of the independent variable.
B)slope to differ for different groups.
C)intercept to differ for different groups.
D)intercept to differ for different values of the independent variable.
Q3) When is it appropriate to include interaction terms in a multiple linear regression?
Explain.Provide an example and discuss the interaction term that you would include and how the relevant estimates would be correctly interpreted.
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Chapter 8: Model Selection in Multiple Linear Regression Analysis
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Sample Questions
Q1) All of the following are potential problems associated with missing data except
A)dropping observations with missing data will bias the estimated coefficients if the missing data is due to selection bias.
B)the number of observations goes down.
C)dropping the independent variables that have missing data will typically bias the estimated coefficients.
D)missing data always increases the estimated standard errors.
Q2) Suppose that you are performing the RESET test for the inclusion of higher-order polynomials and that in the second stage you estimate the sample regression function and the predicted value terms are statistically significant.You decide that
A)higher-order polynomials are not necessary for this regression.
B)you should investigate the inclusion of higher-order polynomials in your regression model.
C)neither regression model is appropriate.
D)higher-order polynomials are never appropriate to include in regression models.
Q3) When would you use the RESET test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.
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Page 10
Chapter 9: Heteroskedasticity
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Sample Questions
Q1) Heteroskedasticity occurs when
A)the error variance is constant.
B)the error variance is non-constant.
C)the dependent variable variance is constant.
D)the dependent variable variance is non-constant.
Q2) The second step in the Goldfeld-Quandt test is to
A)omit the middle c observations from the ordered data set.
B)omit the bottom c observations from the ordered data set.
C)regress the squared residuals on the independent variables from the original OLS regression.
D)regress the squared residuals on the predicted value of the dependent variable from the original OLS regression.
Q3) White's Heteroskedastic standard errors are
A)the preferred method for correcting for potential heteroskedasticity.
B)calculated through an iterative process.
C)automatically calculated in Excel.
D)the result of performing weighted least squares.
Q4) What are the null and alternative hypothesis for testing for the presence of heteroskedasticity? Why? Explain.
Q5) How do you perform the Breusch-Pagan test for heteroskedasticity? Explain.
Page 11
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Chapter 10: Time Series Analysis
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Sample Questions
Q1) What is a time-trend? Why is it important to control for a time-trend if it is present in the data? How can you test and control for a time-trend in your data? Explain.
Q2) A given time-series is said to have a time-trend if
A)an unexpected shift in time-series data.
B)the data trend upward or downward over time.
C)a number of outliers in cross-section data.
D)an independent variable is correlated with the dependent variable but there is no theoretical justification for the relationship.
Q3) What does it mean for a time-series to be stationary? Why is this desirable? Explain.
Q4) A weakly dependent time series is one for which
A)the observations for a given variable become more closely related over time.
B)the probability of distribution of the dependent variable changes over time.
C)the probability of distribution of the dependent variable does not changes over time.
D)the observations for a given variable become less closely related over time.
Q5) How does time-series data differ from cross-section data? Why is this difference important? Explain.
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12
Chapter 11: Auto-Correlation
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Sample Questions
Q1) Autocorrelation occurs when
A)an omitted independent variable is correlated with the error term.
B)the error term is correlated across different time-periods.
C)the error term has a non-constant variance.
D)the error term is,on average,equal to zero.
Q2) What is autocorrelation? Why is it problematic? Explain.
Q3) Write out the model for an AR(1)process.Explain what it means.Repeat for an AR(2)process.
Q4) How do you perform the Durbin-Watson test for autocorrelation? Explain.
Q5) A simple method for determining whether autocorrelation is present in a given data set is to
A)construct a histogram.
B)calculate the variance of the sample.
C)examine the residual plot.
D)plot the data points from smallest to largest.
Q6) What is the intuition behind the Regression test for AR(1)? Explain.
Q7) How do you perform the Regression test for AR(1)? Explain.
Q8) What is the potential shortcoming of the Cochrane-Orcutt method for AR(1)processes? Why is it a concern? How do you correct for it? Explain.
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Chapter 12: Limited Dependent Variables
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Sample Questions
Q1) When using the probit model,estimated marginal effects are obtained by
A)estimating the model by the probit function.
B)converting the estimated coefficients into marginal effects by taking the derivatives of the probit function with respect to the independent variable.
C)estimating the model by OLS.
D)taking the derivative of the estimated coefficients.
Q2) Suppose you are interested in explaining the probability of Switching Jobs as a function of Salary,Experience,Home Ownership,and Number of Children.
a)Write out the regression model that you would want to estimate.Explain the dependent variable in detail.
b)Could you estimate the above model by OLS? What would you call such a model? Are there any potential shortcomings of estimating such a model? If so,what are they? Explain.
c)In reference to your answer in (b),is there an alternative estimator that is more preferred? If so,what is it? Why is it preferred to the model in (b)? Explain.
Q3) What is a multinomial logit model? Why is it more appropriate than OLS? Explain.
Q4) What is a logit model? Why is it more appropriate than OLS? Explain.
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14
Chapter 13: Panel Data
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Q1) What is a random-effects model? How do you estimate such a model? When is it a preferred estimator? Why? Explain.
Q2) Random-effects models are
A)almost never the appropriate model in economics because the unobserved heterogeneity is typically correlated with the independent variables.
B)typically more appropriate than fixed effects models in economics.
C)preferred when the error term is random.
D)difficult to interpret because the coefficient estimates are not true marginal effects.
Q3) Panel data differs from time-series data in that panel data is observed
A)for a number of different individuals in a number of different time-periods.
B)for a given individual in a number of different time-periods.
C)for a number of different individuals in a given time-period.
D)for a given individual in a given time-period.
Q4) Random-effects models improve on pooled cross-section models because they
A)do not take advantage of the panel data nature of the data.
B)have more degrees of freedom available.
C)improve the efficiency of the estimated coefficients.
D)correct for heteroskedasticity.
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Page 15
Chapter 14: Instrumental Variables for Simultaneous
Equations, Endogenous Independent Variables, and
Measurement Error
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Q1) The first-stage in an instrumental variable approach to identify simultaneous equations is to regress
A)the endogenous right hand side variables on the instruments and all exogenous variables.
B)the dependent variable on the predicted endogenous right hand side variables and the exogenous variables in each equation.
C)instrumental variable on all exogenous variables.
D)the exogenous right hand side variables on only the instrumental variables.
Q2) Endogeneity of an independent variable presents a challenge because
A)OLS estimates are biased and inconsistent.
B)it causes the regression to be perfectly collinear.
C)it leads to heteroskedasticity.
D)OLS estimates remained unbiased but they are no longer BLUE.
Q3) Two-stage least squares can be used to
A)identify simultaneous equations.
B)control for heteroskedasticity.
C)account for the time-invariant component of the error term.
D)deal with limited dependent variables.
Page 16
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Chapter 15: Quantile Regression, Count Data, Sample
Selection Bias, and Quasi-Experimental Methods
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Q1) In which of the following cases would you want to use difference-in-difference estimation?
A)When individuals non-randomly select different outcomes of the dependent variable.
B)When you are attempting to replicate a randomized clinical trial.
C)When you are dealing with non-negative count data.
D)When you suspect that the marginal effects are different for different values of the dependent variable.
Q2) In which of the following cases would you want to use a Heckman selection correction model?
A)When individuals non-randomly select different outcomes of the dependent variable.
B)When you are attempting to replicate a randomized clinical trial.
C)When you are dealing with non-negative count data.
D)When you suspect that the marginal effects are different for different values of the dependent variable.
Q3) What is non-negative count data? Why does it present a concern for OLS? How might you control for non-negative count data in the estimation process? Explain.
Q4) What is quantile regression? When might it be preferred to OLS? Explain.
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