Solution for HW 1

Assignment 1 suggested solutions (Tutorial2) Hou Chenxue ECON 6001 Applied Econometrics

October 10, 2014

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Question1(E4.2)

(a) Construct a scatterplot of average course evaluation (Course Eval) on the professor’s beauty(Beauty). Does there appear to be a relationship between the variables? Solution: There appears to be a weak positive relationship between course evaluation and the beauty index.

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Question1(E4.2)

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Question1(E4.2)

(b) Run a regression of average course evaluation (Course Eval) on the professor’s beauty(Beauty). What is the estimated intercept? What is the estimated slope? Explain why the estimated intercept is equal to the sample mean of Course Eval. Solution: \ = 4.00 + 0.133 × Beauty .The variable Beauty has a mean CourseEval that is equal to 0; the estimated intercept is the mean of the dependent variable (Course Eval) minus the estimated slope (0.133) times the mean of the regressor (Beauty). Thus, the estimated intercept is equal to the mean of Course Eval.

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Question1(E4.2)

(c) Professor Watson has an average value of Beauty,while Professor Stock’s value of Beauty is one standard deviation above the average. Predict Professor Stock’s and Professor Watson’s course evaluation. Solution: The standard deviation of Beauty is 0.789. Thus Professor Watson’s predicted course evaluations = 4.00 + 0.133 × 0 = 4.00. Professor Stock’s predicted course evaluations = 4.00 + 0.133 × (0 + 0.789) = 4.105.

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Question1(E4.2) (d) Comment on the size of the regression’s slope. Is the estimated effect of Beauty on Course Eval large or small? Explain what you mean by ”large” or ”small”. Solution: The standard deviation of course evaluations is 0.55 and the standard deviation of beauty is 0.789. A one standard deviation increase in beauty is expected to increase course evaluation by 0.133 × 0.789 = 0.105, or 1/5 of a standard deviation of course evaluations. The effect is small. (e) Does Beauty explain a large fraction of the variance in evaluations across course? Explain. Solution: The regression R 2 is 0.036, so that Beauty explains only 3.6% of the variance in course evaluations. Hou Chenxue (HKU)

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Question2

2.The following graph shows a positive correlation between the strength of state gun laws (how tough state regulation is on gun ownership) and gun violence outcomes across states in the US as of 2012. Does the positive correlation mean that introducing stronger measures to regulate gun ownership can reduce gun violences? Play devil’s advocate and argue that correlation found in the graph might not necessarily imply causation. Note:High rankings on the x axis and the y axis mean strong gun laws and fewer gun violences, respectively. R 2 is the correlation coefficient estimate.

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Question2

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Question2 Solution: Probably there is an omitted variable that affects strength of gun laws and gun violences simultaneously. For example, it is known that more people in the coastal states (northeastern and western states) are progressive and such politcal attitudes are likely to have favored representatives who believe in government’s active role to improve public welfare. Those representatives could have supported strong regulation of gun ownership. At the same time, people in these states are likely to prefer relying on government and public law enforcement to resolve disputes rather than resolving by themselves. Eliminating guns surely reduces gun violences. But the estimated effect of strengthening gun regulation is likely to be biased unless we control for some omitted factors. (Argument with different examples, if shown that a suggested omitted factor satisfies the two conditions for omitted variable bias, is fine.) Hou Chenxue (HKU)

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Question3

(a) Interpret the coefficient estimate on age. Solution: If a person gets one year older, then time he/she spends sleeping increases by 3.54 minutes per week. Hou Chenxue (HKU)

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Question3 (b) It is likely that adults trade off sleep for work. If you are also given the data for time spent working, measured in minutes per week, and include this variable (say totwrok) in the above regression, what would you expect the sign of the coefficient on totwork to be? Solution: Since it is likely that a person working longer sleeps less, the coefficient on totwork will be negative. (c) Part (b) suggests that there might be an omitted variable bias in the original simple regression because totwork is not included. For an omitted variable bias to exist, what additional condition needs to be met? Do you think this condition holds in reality? If yes, what do you expect the sign of the omitted variable bias is? Solution: For an omitted variable bias to occur, totwork must be correlated with age, which is quite plausible. Among adults, it is likely that people work less as they grow old. Therefore totwork and age are likely to be negatively correlated. There exists a positive omitted variable bias. Hou Chenxue (HKU)

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Question4(E6.3) Using the data set Growth described in E4.4, but excluding the data for Malta, carry out the following exercises. (a) Construct a table that shows the sample mean, standard deviation, and minimum and maximum values for the series Growth,TradeShare,YearsSchool, Oil, Rev-Coups ,Assasinations, RGDP60.Include the appropriate unit for all entries. solution:

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Question4(E6.3)

(b) Run a regression of Growth on TradeShare, YearSchool, Rev-Coups ,Assasinations, RGDP60.What is the value of the coefficient on Rev-Coups? Interpret the value of this coefficient. Is it large or small in a real-world sense? Solution: The coefficient on Rev-Coups is -2.15. An additional revolution in one year, reduces the average year growth rate by 2.15% .

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Question4(E6.3) (c) Use the regression to predict the average annual growth rate for a country that has average values for all regressors. Solution: Same as Question1(E4.2) (c). (d) Repeat (c)but now assume that the country’s value for TradeShare is one standard deviation above the mean. Solution: Same as Question1(E4.2) (c). (e) Why is Oil omitted from the regression? What would happen if it were included? Solution: All observations of Oil are 0. So the outcome of regression including Oil is the same as the outcome of regression without Oil.

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Question5(E7.4) Using the data set Growth described in E4.4, but excluding the data for Malta, carry out the following exercises. (a) Run a regression of Growth on TradeShare, YearSchool, Rev-Coups ,Assasinations, RGDP60. Construct a 95% confidence interval for the coefficient on TradeShare. Is the coefficient statistically significant at the 5% level? Solution: The 95% confidence interval is 1.34 ± 1.96 × 0.88 or -0.42 to 3.10. The coefficient is not statistically significant at the 5% level. (b) Test whether, taken as a group,YearSchool, Rev-Coups, Assasinations, RGDP60 can be omitted from the regression. What is the p-value of the F-statistic? Solution: The F-statistic is 8.18 which is larger than 1% critical value of 3.32. Hou Chenxue (HKU)

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