ECOM30002/90002 ECONOMETRICS 2 PRACTICE QUESTIONS
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ECOM30002/90002
ECONOMETRICS 2
PRACTICE QUESTIONS
Question 1.
This question is about the analysis of data on a random sample of 2,061 males, for whom there are observations on:
Wagei |
hourly wage rate in dollars |
Educi |
number of years of education |
Experi |
number of years of work experience |
Metroi |
1 if individual lives in a city/metropolitan area, 0 otherwise |
NearCollegei |
1 if a college/university is present in the local area, 0 otherwise |
Table 1.1 contains regression results that you will use to answer the following questions.
(a) Column (A) of Table 1.1 gives estimates of the Population Regression Function
(PRF)
E(log Wagei |Educi , Experi ) = s0 + s1 Educi + s2 Experi + s3 Experi(2) . (1)
(i) (3 marks) Interpret the significance, sign, and magnitude of the coefficient on Educi .
(ii) (2 marks) Calculate a prediction for the average log Wagei of individuals with
10 years of education and 10 years of work experience. What are the units of measurement of this prediction?
(iii) (2 marks) Is it valid to take the exponential of the prediction in part (ii) to obtain an estimate of the average Wagei of individuals with 10 years of education and 10 years of work experience? Briefly explain why or why not.
(b) Suppose we are interested in estimating the “returns to education”, which is the
causal effect on wages of an additional year of education. Consider a causal repre- sentation for wages of the form
log Wagei = 80 + 81 Educi + 82 Experi + 83 Experi(2) + 84Abilityi + Vi , (2)
where Abilityi is an unobservable factor measuring each individual’s “natural abil- ity” (intelligence, grit, sociability, etc) that may be expected to have a positive effect on their wages, and where Vi represents other unobserved individual factors which are assumed to satisfy
E(Vi |Educi , Experi , Abilityi ) = 0. (3)
Further assume that
E(Abilityi |Educi , Experi ) = 70 + 71 Educi , (4)
so that education may predict ability but experience does not.
(i) (7 marks) Under these conditions, derive the relationships between the coeffi- cients of equations (1) and (2).
(ii) (5 marks) Discuss the implications of your answer to part (i) for using the OLS
estimates of equation (1) as estimators of the causal coefficients in equation (2).
(c) The variables Metroi and NearCollegei , relating to two characteristics of where each individual happens to live, can be considered as possible Instrumental Variables (IV’s) for Educi .
(i) (4 marks) What are the two conditions that must be satisfied for these to be valid IV’s? Give mathematical statements of the two conditions in the modelling context of this question.
(ii) (5 marks) Discuss, briefly and intuitively, whether these two conditions might be satisfied and/or violated in the case of Metroi and NearCollegei .
(d) Consider the results shown in column (B) of Table 1.1.
(i) (4 marks) Interpret the significance, sign, and magnitude of the coefficient 8ˆ1 on Educi .
(ii) (4 marks) Construct a 95% confidence interval for 81 , turn this into a 95%
confidence interval for the marginal effect of education on wages, and inter- pret. The standard errors reported for this regression are heteroskedasticity- consistent — what is the possible consequence for a confidence interval of using a standard error that is not heteroskedasticity-consistent?
(iii) (2 marks) Compare the 8ˆ1 coefficient to sˆ1 on Educi in column (A) of Table
1.1 and explain whether these estimates are consistent with the coefficient relationships derived in part (b)(i).
(e) Both Tables 1.1 and 1.2 provide additional results that permit some statistical eval- uations of the two conditions for the validity of the IV’s Metroi and NearCollegei .
(i) (6 marks) Carry out inference for these two validity conditions. (Be specific about exactly which results in which tables you are using to carry out your inference.)
(ii) (3 marks) Discuss any interpretations of these validity tests for the 2SLS esti-
mates in column (B) of Table 1.1.
(f) (3 marks) Reconsider the prediction you computed in part (a)(ii) of this question,
based on given values of 10 years of education and 10 years of work experience. Assuming good 2SLS estimates of the causal equation (B) in Table 1.1 are given, explain whether or not it would be preferable to replace the prediction from the OLS equation (A) with a prediction from the 2SLS equation in (B).
Table 1.1 Regression results for Question 1
|
(A) log Wagei |
(B) log Wagei |
(C) Educi |
(D) i |
Intercept |
-0.014 (0.094) |
-4.702* (1.138) |
17.491* (0.158) |
-0.030 (0.059) |
Educ |
0.085* (0.005) |
0.347* (0.063) |
|
|
Exper |
0.092* (0.009) |
0.252* (0.041) |
-0.605* (0.036) |
0.000 (0.013) |
Exper2 |
-0.003* (0.000) |
-0.006* (0.001) |
0.013* (0.002) |
0.000 (0.001) |
NearCollege |
|
|
0.365* (0.089) |
-0.069* (0.031) |
Metro |
|
|
0.189* (0 096) |
0.101* (0 033) |
R2 |
0.156 |
-1.132 |
0.373 |
0.006 |
Num. obs. |
2061 |
2061 |
2061 |
2061 |
*p < 0.05
2022-06-05