Assignment #9

PPol 603
Due: Thursday, 8 November 2012

Type up your answers. Give proper credit to those you work with and/or the text(s).

Solve the following problems. Show all of your work, but keep your answers concise. Highlight your (final) answer to distinguish it from your other numbers and text. Include a copy of your input (e.g. do file) or output (e.g. log file), when it is an appropriate way to show your work. However, do not include unnecessary output (i.e. no data dumps), and format any output so that it is easily readable. An appropriate time to include output is when you put your results in a table--if your results are wrong, then graders have no idea how you came to your conclusions (i.e. give partial credit) unless you provide some output. Explanation includes statistical and substantive explanation (explain so that a statistical layperson can understand it, and so that a statistical analyst will see your erudition).

  1. {10 points}
    a. Do Review the Concepts 8.2 in Stock and Watson (p. 296, top of the page).
    b. Do Exercise 8.7 in Stock and Watson.
    c. [adapted from Wooldridge 2013] Suppose the following model is estimated:
    prâte = 97.32 + 5.02mrate + 0.314age − 2.66log(totemp)
    where the data set contains data on various 401k (retirement) plans across for 1534 firms; prate is the participation rate (in percentage), mrate is the firm's 401k match rate, age is how long the 401k plan has been offered, and totemp is the total number of employees of the firm. Interpret the coefficient on log(totemp).
  2. {10} Do Exercises 8.4 and 9.10 in Stock and Watson. For 8.4a and b, calculate the expected change in percentage terms in addition to the expected change in the logarithm.
  3. {40} [adapted from Hill, Griffiths, and Lim 2011] Consider a "life-cycle" model for pizza consumption. We have data on a random sample of 40 individuals, age 18 and older, including their annual expenditure on pizza (pizza), their income in thousands of dollars (income), age (age), and whether the individual is female (female). The data set is found here.
    a. Consider a model without interactions:
    pizza = β0 + β1age + β2income + β3female + u
    What do you expect the signs of the coefficients to be, and why? Run a scatterplot (using scatter or graph matrix) for pizza vs. age and pizza vs. income.
    b. Estimate the model in a. Put your results in a table. Were your expectations in a. confirmed?
    c. Consider a model with interactions:
    pizza = β0 + β1age + β2income + β3female + β4age×income + u
    What do you expect the sign of β4 to be, and why?
    d. Estimate the model in c. Put your results in the same table. Were your expectations in c. confirmed? Is it worthwhile to add the interaction term?
    e. What kind of standard errors are you using? Why? Test whether you can use non-robust standard errors by running a hettest. What do you conclude?
    f. Check for omitted variables in the interaction model with an ovtest. What do you conclude?
    g. Check for other problems in the interaction model by running an rvfplot and using dfbeta. What do you conclude? Note which observations you would drop (if any) by stating values of pizza. (However, in the parts the follow, keep all of the observations in the data set.)
    h. Show how the effect (slope) of income differs by age, by choosing a few values of age and graphing pizza vs. income. Explain in words what the graph shows.
    i. Show how the effect (slope) of age differs by income, by choosing a few values of income and graphing pizza vs. age. Explain in words what the graph shows.
    j. Graph the marginal effect of income at different ages. Explain in words what the graph shows.
    k. Graph the marginal effect of age at different incomes. Explain in words what the graph shows.
    l. Test for multicollinearity using the vif commmand. What do you find? Center both age and income at their means by subtracting its respective average (or closest integer to the average). Re-run part c. using centered age and centered income. What stays the same and changes from d.? Check again for multicollinearity.
  4. {40} Do Empirical Exercises E8.3 and E9.3a in Stock and Watson. Put your results in a table. In E8.3h, use a graph as well as statistical tests to answer the question. Instead of E9.3b, discuss the external validity of extending the findings of E8.3 to Western states.

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