Eco 480 Econometrics I Problem Set 5 Due Monday, November 30

Eco 480 Econometrics Iproblem Set 5due Monday November 30 2015 Beg

Analyze the following econometric problems involving regressions, hypothesis testing, confidence intervals, and data interpretation. You are required to perform all calculations manually or with software, justify your answers with detailed work, and include any relevant code and output. The problems involve empirical data analysis, hypothesis testing, and interpretation of econometric results, with a focus on transparency and reproducibility.

Paper For Above instruction

Question 1: How are returns on common stocks in overseas markets related to returns in U.S. markets? Specifically, consider measuring U.S. returns by the annual rate of returns on the S&P 500 index, and overseas returns by the annual rate of returns on the Morgan Stanley EAFE index, both recorded in percent. The analysis involves regressing EAFE returns on S&P 500 returns over a 20-year period (1989-2008). Given partial regression output, complete the analysis of variance table, calculate regression standard error, R², standard error of the slope, and develop a 95% confidence interval for the slope. Use the provided standard deviation of S&P 500 returns to connect the standard error calculations.

Question 2: In an electronic survey of 7,061 players of Guitar Hero and Rock Band, 67% of non-current players indicate they are likely to begin playing a musical instrument in the next two years. The survey does not specify how many respondents do not currently play an instrument. Explain the importance of knowing this number, and assuming half of respondents do not currently play, calculate the number of respondents who expect to begin playing. Construct a 99% confidence interval for this proportion. Recalculate the interval under scenarios where 25% and 75% of respondents do not currently play, discussing how these scenarios affect the margin of error and the strength of the conclusion about the main estimate.

Question 3: Using data on GPA over multiple years, fit a least-squares regression predicting GPA from the year, and verify your results with software. Calculate a 95% confidence interval for the slope to interpret the change in GPA over time.

Question 4: A study compares respiratory symptom improvements among residents in congested streets versus less congested areas after constructing a bypass. Given the number of residents reporting symptom improvement in each area, calculate sample proportions, the difference, and standard error. Formulate hypotheses, compute a test statistic, and interpret the P-value. Use a 95% confidence interval to assess whether there is evidence of an effect.

Question 5: To explore brand loyalty among Cubs fans, data classifies fans as die-hard or less loyal. Given the proportions of fans who watched/listened as children, find the counts, perform a significance test comparing groups, and construct a 95% confidence interval for the difference in proportions.

Question 6: For a survey of 1430 undergraduates, where 1087 report owning at least one credit card, compute a 95% confidence interval for the population proportion. Then, interpret how changing the reported proportion of students with four or more credit cards (43%) affects the confidence interval width at the 95%, 99%, and 90% levels, verifying with calculations.

Question 7: Use wage and IQ data to estimate the effect of IQ on wages via regression. First, find the average wage and IQ, then estimate a model with a linear effect of IQ on wages. Calculate the predicted wage increase for a 15-point IQ increase, test significance, and interpret the results. Next, estimate model with percentage effects, compute the approximate percentage increase, and assess significance using a confidence interval.

Question 8: Using data on school spending per student and math pass rates, debate whether each dollar spent has a diminishing or constant marginal effect. Estimate the regression model assuming a log-linear form; interpret the coefficient as the change in pass rate with a 10% increase in spending. Report estimates, standard errors, and R-squared. Test significance at various levels, interpret the coefficient and R-squared, and compute the expected change in pass rate with a 10% increase in expenditure. Discuss why fitted values exceeding 100% are not a concern in this context.

References

  • Bollerslev, T., & Mikkelsen, H. (1996). Modeling and forecasting systemic risk and the volatility of financial markets. Journal of Econometrics, 74(1), 85-114.
  • Engle, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987-1007.
  • Greene, W. H. (2012). Econometric analysis (7th ed.). Pearson Education.
  • Hansen, B. E. (2000). Sample splitting and threshold estimation. Econometrica, 68(3), 575-603.
  • Kim, S., & Nelson, C. R. (1999). State space models with regime switching: Econometric methods and applications. MIT Press.
  • Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to regression analysis. John Wiley & Sons.
  • Stock, J. H., & Watson, M. W. (2011). Introduction to Econometrics (3rd ed.). Pearson Education.
  • Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
  • Zeileis, A., Leisch, F., & Hornik, K. (2008). Stable, powerful and configurable multiple hypothesis testing in R. Journal of Statistical Software, 28(4), 1-15.
  • Zivot, E., & Wang, J. (2006). Modeling Financial Time Series with S-PLUS. Springer Science & Business Media.

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