Econ B2000, MA Econometrics
Kevin R Foster, the Colin Powell School at the City College of New York, CUNY
Fall 2019
For this lab, we finally do some regression models to explain wages. We want to understand how important is a college degree (and what major).
Form a group of 3 (again, invite someone new). Groups should prepare a 4-min presentation by one of the group members about their experiment process and results. You get 45 min to prepare.
Make sure you’re stepping up your coding – at minimum, by now you should have your code as R-Script (in top left panel of R Studio) so that you can easily see what you run (CTRL-Enter is an easy shortcut). If you get signficicant errors then stop and re-run your code from a fresh start (clear memory, re-load data) so that you don’t pile one mistake on top of another. When you submit homework, I’ll want to see a file with your code and another with the output from that code. It would be even better to submit an R-Markdown file with code and text, where text tells the story clearly, along with that output – but I understand that not everybody is that far along yet.
As you begin the analysis, you should first consider what subgroup to use – for example, you could run code like this,
attach(acs2017_ny)
use_varb <- (AGE >= 25) & (AGE <= 55) & (LABFORCE == 2) & (WKSWORK2 > 4) & (UHRSWORK >= 35)
dat_use <- subset(acs2017_ny,use_varb) #
detach()
attach(dat_use)This selects people 25-55 (often called prime age), in labor force, working year round, fulltime. Otherwise the regression would be trying to explain why so many people make zero wages despite so many qualifications. (Think through: if you include retirees in the data and estimate a linear model of age affecting wage, what would you expect for the sign of the coefficient?) Of course when you look at college major, you’re looking at only people with at least a college degree but you can code that for yourself.
Make sure you run summary(dat_use) to check for obvious mistakes. Maybe some crosstabs to also look.
First, before running a regression, consider what variables should be in your model. What are some of the important factors that influence a person’s wage? Is there a plausible causal link from X variables to Y and not the reverse?
Now try a linear regression, with wage as the dependent variable, a dummy for major, and other variables of your choice.
For many of the hypothesis tests, you’ll want the AER package
require(AER)Show a plot of regression line with data points, something like this (as suggested in the AER text),
# subset in order to plot...
NNobs <- length(INCWAGE)
set.seed(12345) # just so you can replicate and get same "random" choices
graph_obs <- (runif(NNobs) < 0.1) # so something like just 1/10 as many obs
dat_graph <-subset(dat_use,graph_obs)
plot(INCWAGE ~ jitter(AGE, factor = 2), pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.2), data = dat_graph)
# ^^ that looks like crap since Wages are soooooooo skew! So try to find some sensible ylim = c(0, ??)
plot(INCWAGE ~ jitter(AGE, factor = 2), pch = 16, col = rgb(0.5, 0.5, 0.5, alpha = 0.2), ylim = c(0,150000), data = dat_graph)
# discus what you see in this plot
# change this line to fit your regression
to_be_predicted2 <- data.frame(AGE = 25:55, female = 1, AfAm = 0, Asian = 0, Amindian = 1, race_oth = 1, Hispanic = 1, educ_hs = 0, educ_somecoll = 0, educ_college = 1, educ_advdeg = 0)
to_be_predicted2$yhat <- predict(model2, newdata = to_be_predicted2)
lines(yhat ~ AGE, data = to_be_predicted2)Create some more, for different X-values.
Carefully explain the hypothesis tests of each coefficient and all of the coefficients jointly. For each coefficient, explain the t-stat, p-value, and confidence interval.
Show how heteroskedasticity-consistent standard errors, as with coeftest(model1,vcovHC), would affect each of these.
Try both lm(INCWAGE ~ … and lm(log(INCWAGE) ~ … Compare mean of predicted values of first version with exp(x) mean of predicted values of second version. Discuss.
Finally, always, always, ALWAYS !! remember this part,
detach()You might do that multiple times, if you were careless previously…
Try some more linear regressions. Explain if there is a plausible causal link from X variables to Y and not the reverse. Explain what additional restrictions to put on the dataset (eg just prime age, just females, just college degree, whatever).
Explain your results, giving details about the estimation and providing any relevant graphics. What are the changes from previous regression on state-level averages and why might this be so? How do changes in specification (e.g. logs) change the estimated coefficients? What are some relevant predicted values? Do those seem sensible? What additional information would be useful? Impress me.