PROBLEM SET #1 – LEGON CAMPUS
- Omitted variable bias is a potential problem because it
a)prevents accurately estimating true marginal effects.
b)results in estimated standard errors that are too large.
c)results in inefficient parameter estimates.
d)might highlight spurious correlations.
- Endogeneity of an independent variable occurs when
a)an independent variable is correlated with the dependent variable.
b)an independent variable is correlated with the error term.
c)the dependent variable is correlated with the error term.
a)the dependent variable is correlated with an independent variable.
- Inclusion of irrelevant variables is a potential problem because
a)results in biased estimated slope coefficients.
b)might highlight spurious correlations.
c)results in estimated standard errors that are too large.
d)prevents accurately estimating true marginal effects.
- The second-stage in an instrumental variable approach to controlling for endogenous independent variables is to
a)regress the endogenous independent variable on the instrument and all of the remaining independent variables and using those estimates to calculate predicted values of the endogenous variable.
b)estimate the original population regression model with the residuals included as an independent variable.
c)estimate the original population regression model with the predicted values of the endogenous right hand side variable substituted for the observed values of the endogenous right hand side variables.
d)regress the endogenous variable on the instrument and all of the remaining independent variables and using those estimates to calculate the residuals.
- Measurement error in an independent variable occurs when
a)the dependent variable is uncorrelated with the error term.
b)the true value of the independent variable is observed.
c)the true value of the left hand side variable is not known.
d)the variable is measured with error such that and is the true value of the variable.
a).
- The RESET test is used to
a)test for the inclusion of higher-order polynomials.
b)test for choosing between non-nested models.
c)test for the individual significance of coefficients.
d)test for omitted variable bias.
- 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.
Short Answer Questions
- Suppose you are a potential college student that is interested in determining whether it is worthwhile to declare a certain major. In an effort to find the answer, you collect data on 1,247 college who majored in HUMANITIES, SCIENCE, ENGINEERING, or ENGLISH and you estimate the sample regression function (standard errors in parentheses)
a)Do you think omitted variable bias is a potential problem in this case? Why? Explain.
b)What is the problem associated with omitted variable bias? Explain.
c)How might you control for the potential omitted variable bias in this case? Explain.
- When would you use the Davidson-MacKinnon test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.
- Suppose you are interested in estimating how the test scores of elementary schools are related to average class size, parents education level (in years), and percent of English learners at the school. To do so, you collect a sample of 200 California public schools and specify the following model:
Suppose you are concerned that the proposed model needs higher order polynomials.
a)After thinking about it, you believe that all of the independent variables may need to be entered in as a higher order polynomial. What type of test would you perform? Describe the steps you would take to implement this test.
b)Now instead you believe that the model estimated above is not appropriate and a better model would be
How would you test between the initial model and this model? Be as specific as possible.
- Suppose your model below satisfies all the classical linear regression model assumptions
You are interested in the effect of WAEC scores on college GPA. Suppose that WAEC scores and Family size are uncorrelated and you estimate by regressing CGPA on only WAEC score (so Family Size is not included in the regression). Does this estimator suffer from omitted variable bias? Explain using the Ballentine
- Explain why two perfectly multicollinearregressors cannot be included in a linaer multiple regression
- Suppose that you wish to estimate a model to explain the final exam score (finscore) in Econ 444 in terms of percentage of classes attended (attend), prior college GPA (PCGPA) and WAEC aggregate score (WAEC)
(i)Let dist be the distance between the students’ living quarters to the N Block lecture hall. Do you think distis uncorrelated with ε? Explain
(ii)Assuming that distand ε are uncorrelated, what other assumptions must dist satisfy to be a valid instrumental variable for attend?
(iii)Assuming that PCGPA and WAEC are exogenous, how would you employ the 2SLS (two stage least squares) estimation technique on this model? Explain
7,Consider a model where the explanatory variable has a classical measurement error
(1)
(2)
Assume u has zero mean and is uncorrelated with X* and ε. We observe Y and X only. Assume that ε has mean zero and is uncorrelated with X* and that X* has zero mean,
a)Write X*=X- and plug into equation (1) above and show that the error term in the new equation is negatively correlated with X if