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Stata Assignment 1

Econ 120B Spring 2022

• You should submit your answers on Canvas, including your do-file.

• The deadline of submitting this Stata Assignment is April 22, 11:59pm. No late submission will be accepted.

• This Stata Assignment will be graded on three scales: 0%, 5%, and 10%. (For example, if you are able to answer more than half of the questions correctly, your will get the full credit for this assignment.)

• If your do-file does not run, we will subtract 2.5%.

• Name your do-file with your PID, such as “A12345678.do”. Start your do-file with the following (also include your name and PID in your do-file)

/*******************************************************************************

ECON 120B, Spring 2022

Stata Assignment 1

Name:

PID:

*******************************************************************************/

clear all // clear the environment/memory

set more off

sysuse nlsw88 // load the built-in dataset nlsw88

Please make sure your do-file is reasonably documented to help us understand your code.

• nlsw88 is a built-in dataset that comes with Stata. It is an extract from the 1988 round of the National Longitudinal Survey of Mature and Young Women. Following is a summary of the variables in this dataset.

idcode                     survey id

age                         age

race                        race, can take three values, white, black or other

married                   = 1 if is currently married, = 0 otherwise

never_married          = 1 if never married, = 0 otherwise

grade                      current grade completed

collgrad                   = 1 if graduated from college, = 0 otherwise

south                      = 1 if lives in southern states, = 0 otherwise

smsa                      = 1 if lives in standard metropolitan statistical area, = 0 otherwise

c_city                     = 1 if lives in central city, = 0 otherwise

industry                  industry, use tab industry to see the categories

occupation              occupation, use tab occupation to see the categories

union                      = 1 if is in a union, = 0 otherwise

wage                       hourly wage, measured in $

hours                       hours worked per week

ttl_exp                     total work experience, measured in years

tenure                     current job tenure, measured in years

More information on the original data can be found here:

https://www.bls.gov/nls/orginal-cohorts/mature-and-young-women.htm

1. In this exercise you will re-label variables and create some new variables which will be used later.

(a) Re-label the variable smsa to live in urban areas so that it is more informative. Note that SMSA stands for “standard metropolitan statistical area.”

(b) Re-name the variable smsa to urban.

(c) Generate a new variable called wagecopy taking the same values as the variable wage, so that we can modify the wage data without loosing the original variable.

(d) The minimum wage in 1988 was $3.35 an hour. Let’s say our fictional bosses at the Bureau of Labor Statistics will be mad if they see evidence of minimum wage law violations in the dataset. In wagecopy, replace wagecopy with 0 for workers that earned strictly less than $3.35 an hour.

(e) How many observations are in this dataset?

(f) How many missing observations are in wagecopy?

(g) Generate a variable called lnwagecopy which is the natural logarithm of wagecopy.

(h) How many missing observations are in lnwagecopy? Why does this make sense?

2. In this exercise, you are asked to compute some simple summary statistics using the binary variable collgrad, contained in the dataset.

(a) Use the command tabulate to show the two categories of the variable collgrad and their frequencies. What is the proportion of the category not college grad? Please report a number between 0 and 1.

(b) Use the same command, this time specifying the option nolabel, to visualize the numeric values corresponding to the different categories of collgrad. Which numeric value corresponds to the label college grad?

(c) Use the command summarize to compute the sample mean of collgrad. After executing summarize, Stata stores temporarily the sample mean in the object r(mean). To see this, generate a scalar variable collgrad_mean equal to r(mean), by typing scalar collgrad_mean = r(mean) in the line just after the command summarize. Finally, display the variable value by typing display collgrad_mean, and verify that the value displayed is the same as the one returned by the command summarize. What is the sample mean of collgrad? What is its relation to your answer in 2(a)?

(d) Repeat the steps of 2(c), this time to create a scalar variable, collgrad_var, containing the sample variance of collgrad. What is the sample variance of collgrad? (Hint: after running the summarize command, you can find the sample variance by r(Var)).

(e) Compute the sample variance of collgrad without the summarize command, using only the variable collgrad_mean. (Hint: you can think of collgrad as drawn from a Bernoulli distribution with parameter p, where p is the prob-ability of having a college degree. The (population) variance of a Bernoulli random variable is p(1 − p). What is the relation between p and the sample mean collgrad_mean? Finally, remember that the sample variance can be obtained starting from the formula of the population variance by replacing the population mean with the sample mean.)

3. The following problems provide more practice using conditional statements to tabulate and summarize variables.

(a) Among unmarried people, what is the fraction of those who were married before? You should report a number between 0 and 1. (Hint: use the variables, married and never_married.)

(b) What is the difference in average hours worked for married and unmarried workers? Please report a positive number. (Hint: use the variables married and hours.)

(c) What is the average hours worked for unmarried college graduates with strictly more than 8 years of experience? (Hint: use the variables married, collgrad, ttl_exp, and hours.)

(d) Among those living in urban areas, what is the fraction of laborers? Please report a number between 0 and 1. (Hint: use the variables occupation and urban. In addition, missing values should not be counted in your calculation.)

(e) Use the variable wagecopy. Among unionized workers, what is the fraction of those who earn strictly more than $6.5 an hour? Please report a number between 0 and 1.

4. This exercise refers to the following model:

wagei = β0 + β1gradei + ui,

where the wage of individual i is regressed on his/her highest grade completed and a constant term. You are asked to compute the intercept and slope estimates in a variety of ways, and compare your results in each case. First, use the command

keep if !missing(wage, grade)

to drop people with missing wage or grade from the dataset.

(a) How many observations were dropped?

(b) Use the regress command to estimate the coefficients βˆ0 and βˆ1. What is the value of βˆ0? What is the value of βˆ1? (Hint: type regress wage grade, the constant term will be added automatically to the regression. To find βˆ0, check the row labeled by cons and the column labeled by Coef.)

(c) You are now asked to compute the same estimates using a different procedure:

• Compute the sample covariance between wage and grade, and the sample variance of grade, and save them in two scalars, cov_wg and var_g. (Hint: you can compute the variance-covariance matrix using the corr command, with the option covariance. For instance, if you type corr wage grade, covariance, the output will be a matrix containing the variance of wage, the variance of grade and the covariance between wage and grade.

On a related note, the three values will be stored in r(Var_1), r(Var_2) and r(cov_12), respectively. You can check the list of stored objects by typing return list just after running the corr command.)

• Generate the scalar beta_1 equal to cov_wg / var_g and display it by typing display beta_1. What is the relation between this estimate for β1 and the one in 4(b)?