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ECMT6007/6702: Econometric Applications Problem Set 6
发布时间：2022-11-18
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ECMT6007/6702: Econometric Applications
Problem Set 6
Semester 2 2022
Question 1. Measurement Error
(i) What is‘attenuation bias’and what is the cause of this problem?
(ii) The following equation explains weekly hours of television viewing by a child in terms of the child’s age, mother’s education, father’s education, and number of siblings:
tvhours* = β0 + β1 age + β2 age2 + β3 motheduc + β4 fatheduc + β5 sibs + u
We are worried that tvhours* is measured with error in our survey. Let tvhours be the reported hours of television viewing per week in the survey. Under what circumstances will measurement error in tvhours not cause bias in the estimation of the model by OLS using the survey data? Explain you reasoning.
Question 2. OLS Specification Tests and Quantile Regression
(i) Download the dataset wage6.dta from the course Canvas site and estimate the sample mean,
minimum, maximum and standard deviation for each of the variables.
log (wage) = β0 + β1 educ + β2 exper + u (1)
and report the results in the standard form.
(iii) Apply the RESET Test to model (1) using a 1% significance level. Present the formal hypothesis
test. Is there evidence of neglected nonlinearities in the model specification?
(iv) An alternative model where education and experience are expressed in log-form is the follow- ing specification:
log (wage) = β0 + β1 log (educ) + β2 log (exper) + u (2)
Use Method 1 for non-nested specification tests (based on the construction of a comprehen- sive model for log (wage)) and test whether the log or level specification for the explanatory variables is superior (use a 5% significance level). Which specification of the model, (1) or (2), is superior?
[Extention: redo the specification testing using Method 2: which specification does this ap- proach support?]
(v) We are concerned that omitted ability will cause bias in the estimation of the return to edu- cation. One way to address this problem is to include a proxy for ability. Use two variables KWW (the‘Knowledge of the World of Work’test score) and IQ test score as a proxy for ability in the wage equation:
log (wage) = β0 + β1 educ + β2 exper + β3 KWW + β4 IQ + u (3)
Are IQ and KWW jointly significant? Test this joint hypothesis using a 1% significance level.
(vi) What is the 95% confidence interval for β1 from model (3)? What has happened to the esti- mated return to education with the inclusion of both proxy variables?
(vii) Estimate the model specification in (3) using the quantile regression estimator for quantiles τ = (0.1, 0.25, 0.5, 0.75, 0.9). Report the estimates of β1 (and the bootstrap standard error) in a table. Are the set of quantile regression estimates for β1 similar to the OLS estimate of β1 ?
Is there a pattern across quantiles?
[Hint: use the Stata command sqreg]
(viii) Re-estimate the quantile regressions in (vii) with the number of bootstrap repetitions set to 100 (use the option reps(100)). Does this change the magnitude of the standard errors, and the statistical significance, of any of the coefficients?
(ix) Test whether the return to education is uniform across all the quantiles examined. What do you conclude?
The STATA command to do this is:
test [q10]educ = [q25]educ = [q50]educ = [q75]educ = [q90]educ
Note: The wage6.dta dataset can be downloaded from the course Canvas site. The data set has 935 observations and 5 variables. The variables are:
• wage level (in $)
• IQ score
• KWW‘Knowledge of the World of Work’test score
• educ (years of completed education)
• exper (years of work experience)
