PS7

Instructions

Create a new markdown document where you will answer all questions. Submit (1) your code as an .Rmd file, and (2) a rendered html file including only what you wish to present, to the Problem Set 7 assignment under the Assignments tab in Canvas. The problem set is due Friday, 21 March, by 10:00 EST. Name your files lastname_ps07 (.html and .Rmd).

All submitted work must be your own.

Data for Problem 1

You will use the data file chile.csv. These are data on citizen characteristics and public opinion in Chile in 1988. The variables of interest are as follows:

  • age: age, in years
  • population: population size of respondent’s community
  • statusquo: higher values = more support for the status quo, standardized to have mean zero and standard deviation of one
  • income: monthly income, in pesos
  • education: 3 levels: primary only (P), post-secondary (PS), secondary (S)
  • sex: factor variable with two levels, female (0) and male (1)
  1. Load the data and save it in an object named chile
  2. Create a new variable, income_1000, that measures income in thousands of pesos
  3. Create a new variable, educ_num, that is numeric, with increasing values representing increasing amounts of education (use values 0, 1, and 2)
  4. Create a new variable, pop_1000, that measures population in thousands of people

Problem 1

\[ \text{statusquo}_i = \beta_0 + \beta_1\text{age}_i + \beta_2\text{sex}_i + \beta_3\text{income_1000}_i + \beta_4\text{educ_num}_i + \\ \beta_5\text{population_1000}_i + \beta_6(\text{income_1000}_i)(\text{educ_num}_i) + u_i \]

  1. Estimate the model above using lm, store it in object m1, and report your OLS regression results in a professional looking table.

  2. What is the p-value for the estimate for \(\beta_6\) and what does it tell you about its associated null hypothesis test? Write a sentence that interprets this test substantively. Be specific with respect to the variables involved: what does this null test mean for the variables and their relationships to the DV?

  3. Write (using Latex) the equation for the conditional marginal effect of education on support for the status quo.

  4. Use this formula to calculate the set of conditional marginal effects across the range of values of income in these data (income from min to max). Plot these conditional marginal effects in a professional-looking figure.

  5. Use the analytic formula for the standard error of the conditional marginal effect to calculate 95% confidence bounds by hand for the estimates you calculated in part c., and add these to your plot. (show using echo=T)

  6. Write a substantive interpretation of the plot. What does the data tell you about the effect of education and how it is conditioned by income?

  7. Use the marginaleffects package to check your work for c. and d. Make sure you get the same result by hand and using marginaleffects.

  8. By hand, calculate bootstrapped standard errors for the coefficients on the two constituent terms of the interaction and for the interaction term itself. Calculate 95% confidence intervals for each using the percentile method.

  9. Do the same thing as in h., but using the marginaleffects package function inferences() and the bootstrap options therein.

  10. Now use the boot package to calculate 95% confidence intervals for \(\hat{\beta_3}\) using the accelerated bias-corrected approach (bca).

Data for Problem 2

We will use the following variables in the dataset contribupdate.csv:

  • age: Age (years)
  • female: 1=female, 0=male
  • faminc: Household income (in $1,000 U.S. dollars);
  • given: Campaign contributions over the past year (in U.S. dollars).
  1. Load the data and name it contrib.
  2. Create two new variables that are the natural log transform of faminc and given, and name them ln_faminc and ln_given, respectively.

Problem 2

\[ \ln(\text{given}_i) = \beta_0 + \beta_1 \text{age}_i + \beta_2 \text{female}_i + \beta_3 \ln(\text{faminc}_i) + u_i \]

  1. Estimate the model above using lm and store it in the object m2.

  2. Calculate the following quantities by hand (show using echo=T):

    • The predicted percent change in given for a 10-year increase in age
    • The difference in the expected values of given for females versus males, holding age and faminc at their respective means.
    • The average marginal effect of faminc on given.

  3. Use simulation (use sim function in arm package) to get 95% confidence bounds for each of the quantities you calculated in part b. (show using echo=T)

  4. Write a short substantive interpretation of the results for each of these quantities and their respective confidence intervals.