Econ B2000, MA Econometrics

Kevin R Foster, CCNY

  1. What are the names of the people in your study group?

  2. Using the CPS data, construct some interesting regressions on wage and salary (you might use the same subgroup as I did or you might change it up). Estimate a linear, quadratic, cubic and quartic specification of age on log wage. Don’t just give me raw output! Make a nice table, like stargazer or in Stock and Watson (e.g. Chapter 9, Table 9.2). Make nice graphs and tests of groups of coefficients like I showed in class. Explain your regressions and what you learn.

  3. Look at averages by educational attainment and discuss how these relate to the results from your previous regression. What does OLS contribute; how does it change the simple results from differences in means?

  4. Consider the following table of numbers of people (from CPS data) who make under or over $15/hr in wage - a level that some politicians want to set as the new minimum wage. (This is a particular subset, don’t bother trying to replicate, the numbers given here should be sufficient.)

number Native Immigrant Native Immigrant
Educ HS or more 14235 3113 33150 5296
no HS diploma 1062 1824 662 567
  1. Is the fraction of immigrants making less than $15/hr different from the fraction making more than $15/hr? In a statistical test of the difference, what is t-statistic, p-value, and confidence interval?

There are 4937 making less than 15 and 5863 making more, so this is 0.4571296 vs 0.5428704. The standard error of the sample proportion is sqrt(p(1-p)/n) so 0.0047935. The difference of either fraction from 50% is much larger so the t-stat is 8.9433733 and the p-value is much less than 1%, 0.

  1. Is the fraction of people without a HS diploma, making less than $15/hr, different from the fraction making more than $15/hr? In a statistical test of the difference, what is t-statistic, p-value, and confidence interval?

There are 2886 with less than HS making less than 15 and 1229 with less than HS making more, so this is 0.7013366 vs 0.2986634. The standard error of the sample proportion is sqrt(p(1-p)/n) so 0.0071346. The difference of either fraction from 50% is much larger so the t-stat is 28.2197608 and the p-value is much less than 1%, 0.

  1. In the population of people making less than $15/hr, what fraction are immigrants without a HS diploma?

The fraction is 0.0990766.

  1. What is the conditional probability of finding an immigrant without a HS degree, given that the person is an immigrant and is making less than $15/hr?

The conditional probability is 0.3694551.

  1. What is the conditional probability of finding an immigrant without a HS degree, given that the person is an immigrant and is making more than $15/hr?

The conditional probability is 0.0967082.