Problem Set 4

This problem set will revisit some of the material covered in Handouts 3 and 4. You will be required to work with a ‘raw’ dataset, downloaded from an online repository. For this reason, you should take care to check how the data is coded.

You will be using a version of the US Current Population Survey (CPS) called the Merged Outgoing Rotation Group (MORG). This data is compiled by the National Bureau of Economic Research (NBER) and has been used in many famous studies of the US economy. The CPS has a rather unique rotating panel design: “The monthly CPS is a rotating panel design; households are interviewed for four consecutive months, are not in the sample for the next eight months, and then are interviewed for four more consecutive months.” (source: IPUMS). The NBER’s MORG keeps only the outgoing rotation group’s observations.

The MORG .dta files can be found at: https://data.nber.org/morg/annual/.

Preamble

Create a do-file for this problem set and include a preamble that sets the directory and opens the data directly from the NBER website. Of course, this requires a good internet connection. For example,

clear 
//or, to remove all stored values (including macros, matrices, scalars, etc.) 
*clear all

* Replace $rootdir with the relevant path to on your local harddrive.
cd "$rootdir/problem-sets/ps-4"

cap log close
log using problem-set-4-log.txt, replace

use "https://data.nber.org/morg/annual/morg19.dta", clear

You can, of course, download the data and open it locally on your computer.

Questions

1. Create a new variable exper equal to age minus (years of education + 6). This is referred to as potential years of experience. Check how each variable defines missing values before proceeding. You will need to create a years of education variable for this. Here is he the suggested code:

tab grade92, m
gen eduyrs = .
    replace eduyrs = .3 if grade92==31
    replace eduyrs = 3.2 if grade92==32
    replace eduyrs = 7.2 if grade92==33
    replace eduyrs = 7.2 if grade92==34
    replace eduyrs = 9  if grade92==35
    replace eduyrs = 10 if grade92==36
    replace eduyrs = 11 if grade92==37
    replace eduyrs = 12 if grade92==38
    replace eduyrs = 12 if grade92==39
    replace eduyrs = 13 if grade92==40
    replace eduyrs = 14 if grade92==41
    replace eduyrs = 14 if grade92==42
    replace eduyrs = 16 if grade92==43
    replace eduyrs = 18 if grade92==44
    replace eduyrs = 18 if grade92==45
    replace eduyrs = 18 if grade92==46
    lab var eduyrs "completed education"
tab grade92, sum(eduyrs)

2. Keep only those between the ages of 18 and 54. Check the distribution of `exper’ and replace any negative values to 0.

3. Create a categorical variable that takes on 4 values: 1 “less than High School”; 2 “High School Diploma”; 3 “some Higher Education”; 4 “Bachelors”; 5 “Postgraduate”. This variable should be based on the the grade92 variable. You can find the value labels for this variable in this document: https://data.nber.org/morg/docs/cpsx.pdf. I suggest using the recode command, which allows you to create value labels while assigning values. Check the distributio of exper by education category.

4. Create the variable lnwage equal to the (natural) log of weekly earnings. Create a figure that shows the predicted linear fit of lwage against exper, by educat. Try to place all 5 fitted lines in the same graph.

5. Estimate a linear regression model that allows the slope coefficient on exper and constant term to vary by education category (educat). Let the base (excluded) education category be 2 “High School diploma”.

\[ \ln(Wage_i) = \alpha + \sum_{j\neq2}\psi_j \mathbf{1}\{Educat_i=j\} + \beta Exper_i + \sum_{j\neq2}\gamma_j Exper_i\times\mathbf{1}\{Educat_i=j\}+\upsilon_i \]

6. Show that after 13 years of experience, those with some Higer Education (but no Bachelors), out earn those with just a high school diploma. You can assume that there are is a 2 year difference between the experience (education).

7. Use the post-estimation test command to test the null hypothesis: \(H_0: 15\beta = 13(\beta+\gamma_3)+\psi_3\).

8. Estimate a transformed version of the above model allowing you to test the above hypothesis using the coefficient from a single regressor. That is, the resulting test should be a simple t-test of \(H_0: \phi=0\), where \(\phi\) is the coefficient on the interaction of exper and a dummy variable for educat=3. This will be easier to do if you estimate the model using only the relevant sample: those with High School diplomas and some Higher Education. I suggest avoiding the use of factor notation to create the dummy variables and interaction terms for this exercise. For example, the following should replicate the relevant coefficients from Q5.

gen hasHE = educat==3 if inlist(educat,2,3)
gen hasHEexp = hasHE*exper

reg lnwage exper hasHE hasHEexp

9. Verify that the F-statistic from Q7 is the square of the above T-statistic.

10. Use the restricted OLS approach to replicate the F-statistic and p-value from Q7.

11. Use the restricted OLS approach to test the following hypothesis corresponding to the model in Q5:

\[ H_0: \gamma_j = 0\qquad \text{for}\quad j=1,3,4,5 \] Compute the F-statistic and p-value. Verify your result using the post-estimation test command.

12. Compute the relevant Chi-squared distributed test statistic and corresponding p-value for the above test, assuming \(n\) is large (enough).

13. Using the data from Problem Set 2, estimate the simple linear regression model using OLS,

\[ \ln(Wage_i) = \beta_0 + \beta_1 Educ_i + \beta_2 Female_i + \varepsilon_i \]

14. Estimate the model using Maximum Likelihood. Take a look at https://www.stata.com/manuals13/rmlexp.pdf, the documentation for the mlexp command. It has a discussion on estimating the CLRM using ML.1

15. Estimate the model using Method of Moments. You can use the gmm command in Stata. Hint: the regressors will be their own instruments and use the onestep option.2

Postamble

log close

Footnotes

  1. You can also look at the following resource for a more flexible approach to ML estimation in Stata: https://www.stata.com/features/overview/maximum-likelihood-estimation/↩︎

  2. Here is a resource on GMM in Stata: https://www.stata.com/features/overview/generalized-method-of-moments/↩︎