Assignment instructions

•   You must submit your work via the Turnitin link on Moodle by 16:00 on Friday March 8,2024.

•   This assignment will be marked for the course assessment and will be worthI 10% of your final mark. You must attach your Stata do-file to your answers (by typing Stata codes or pasting screenshots of the do-file window or the result window in your answer) and failure to do so will result in a zero mark for the computing questions.

•   Name, student number, course title, tutorial group number and tutor’s name should be clearly included in the submission. Your answers including Stata do-file should not exceed 6 pages. The Assignment is based on the material covered in both lectures and tutorials up to the end of Week 3.

•   The assignment is INDIVIDUAL work. You may discuss the assignment with your peers, but you must submit YOUR OWN answers.

•   If the answer requires some mathematical calculation show the steps, don’t just report the final results.

•   This assignment has a total of 88 points awarded.

One core question in Labor Economics is the relationship between an individual's skills and their wage. In this exercise, we will explore this relationship using the "multidimensional.dta" dataset, which comprises data for 1,260 workers. The outcome variable, "wage," denotes the hourly wage rate ($/hour).

For this exercise, we will start with the most conventional proxy for skills: years of schooling, represented by "educ."

Additionally, the dataset encompasses various other variables that we will examine, including "noncog", which assesses noncognitive skills on a scale from 0 to 4, with 4 indicating the highest level of skill, a gender dummy variable ("female"), and location variables indicating residence in the South ("south") or a big city ("bigcity"). The dataset also contains information on the industry of employment, specifically whether an individual works in the service industry ("service"). Descriptive statistics for these variables are provided in Table 1.

Table 1: Descriptive Statistics

1. [6pts] Using the data in multidimensional.dta, run a simple linear regression of wage on educ:

wage = a0  + a1 Educ +  U           (1)

and estimate by OLS. Report the results in equation form, including the sample size and R2 .  Assume that the Gauss-Markov assumptions 1-4 hold and interpret the estimated coefficient a1(̂) .  (Please pay attention to the unit of measurement  when interpreting the coefficient).

2. [6pts] Let’s consider another functional form, the log-linear model:

log(wage) = β0  + β1 Educ +  U           (2)

Estimate model (2) by OLS and report the results in equation form, including the

sample size and R2 . Assume that the Gauss-Markov assumptions 1-4  hold and

interpret the estimated coefficient β1(̂) . (For your convenience I already generated

log(wage) (lwage). Log here refers to the natural logarithm).

3. [8pts] In addition to the two regression models we’ve discussed, there are other possible regression models between wage and educ. For each of the following models, determine if it is a linear regression model.

log(wage) = β0  + Educβ1   +  Z           (a)

wage = β0  + β1 Educ + β2 Educ2  +  w           (b)

1/wage = β0  + β1 Educ +  β2service + β3 Educ ∗ service +   Q           (c)

log(wage + β0) = β1 Educ +  U           (d)

4.  [10pts]  Explain the meaning of the zero-conditional-mean assumption for the simple linear regression in Model (1) (from Q1), both mathematically and in plain language (please be sure to include both the mathematical expression and a clear explanation of what the assumption represents in this example). Provide one possible reason why the zero-mean condition (ZMC) might NOT hold in Model (1). Interpret a1(̂) in model (1) if the “zero conditional mean assumption” did NOT hold.

5.  [18pts] Recent  literature has broadened the scope of skill measurement from a unidimensional concept to a multidimensional concept. Considering an occupation as a collection of tasks, it is logical to conceptualize skills as a portfolio possessed by an individual, with the returns on different skill dimensions varying across markets. In  this exercise, we adopt a simplified approach by modeling skills in two dimensions: cognitive and noncognitive skills. The previously mentioned "educ" variable serves as  a proxy of cognitive skills. To incorporate a measure of individuals' noncognitive skills, we introduce a control variable ("noncog") in Model (2), representing skills that  encompass social interactions, physical tasks, strength, and eye-hand coordination etc.. For this problem, assume that the Gauss-Markov assumptions 1-5 hold for this new  model.

log(wage) = Y0  + Y1 Educ + Y2 Noncog +  U            (3)

a.  Estimate the extended model and present the results in equation form, including the sample size and  R2 .

b. Interpret the two coefficients of educ and noncog,  Y1(̂)   and  Y2(̂)   respectively.

c. Compare  Y1(̂)   to  β1(̂)   obtained in question 2 (from model (2)).