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ECONOMETRICS AND BUSINESS STATISTICS

APPLIED ECONOMETRICS

Tutorial 6

QUESTION 1

A researcher (A) obtains data on household annual expenditure on books, B, and annual household income, Y, for 200 UK households in 2021. She hypothesizes that B is related to Y and the average cognitive ability of adults in the household, IQ, by the relationship

log B = Pi + 庆 log Y + 月3 log IQ + u (1.A)

where u is a disturbance term or regression error that satisfies the standard multiple regression model assumptions. Another researcher (B) also considers the possibility that log B may be determined by log Y but he could not obtain the data IQ for his research and hence his regression model is:

log B = Pi + % log Y + £ (1.B)

i. e. regress log B on log B alone and £ is a regression error.

In the sample the correlation between log Y and log IQ is 0.86. Researcher A performs the following regression: log B on both log Y and log IQ, and Researcher B performs the following regression: log B on log Y only, with the results shown in the table (standard errors in parentheses):

Table 1: Regression results

1. Briefly explain “endogeneity” IN WORDS (Not a single mathematical symbol or expression with not more than three sentences).

2. Explain whether you would expect the coefficient of log Y in each regression (1.A) and (1.B) to be greater or smaller than or equal to the true parameter value in regression (1.A) with mathematical evidence and justification. Briefly discuss the consistency of each coefficient estimator for p2 in the regression (1.A) and (1.B).

3. Suppose that Researcher B considers mother's education (years of schooling), mEDUC as an instrument. Provide conditions for a valid instrument and discuss these in the context of mEDUC for Researcher B.

4. Provide the instrumental variables estimator for for Researcher B and show its consistency when mEDU C is a valid instrument for the regression (1.B) with mathematical evidence and justification.

QUESTION 2

10.18 Consider the data file mroz on working wives. Use the 428 observations on married women who participate in the labor force. In this exercise, we examine the effectiveness of a parent's college education as an instrumental variable.

a. Create two new variables. MOTHERCOLL is a dummy variable equaling one if MOTHER- EDUC > 12, zero otherwise. Similarly, FATHERCOLL equals one if FATHEREDUC > 12 and zero otherwise. What percentage of parents have some college education in this sample?

b. Find the correlations between EDUC, MOTHERCOLL, and FATHERCOLL. Are the magnitudes of these correlations important? Can you make a logical argument why MOTHERCOLL and FATHERCOLL might be better instruments than MOTHEREDUC and FATHEREDUC?

c. Estimate the wage equation in Example 10.5 using MOTHERCOLL as the instrumental variable. What is the 95% interval estimate for the coefficient of EDUC?

d. For the problem in part (c), estimate the first-stage equation. What is the value of the F-test statistic fbr the hypothesis that MOTHERCOLL has no effect on EDU Cl Is MOTHERCOLL a strong instrument?

e. Estimate the wage equation in Example 10.5 using MOTHERCOLL and FATHERCOLL as the instrumental variables. What is the 95% interval estimate for the coefficient of EDUC? Is it narrower or wider than the one in part (c)?

f. For the problem in part (e), estimate the first-stage equation. Test the joint significance of MOTHERCOLL and FATHERCOLL. Do these instruments seem adequately strong?

g. For the IV estimation in part (e), test the validity of the surplus instrument. What do you conclude?