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)?
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