Explain the effect of age on children by interpreting the estimates of β2, and β3.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1: 

Use the dataset FERTIL2x.DTA for this question. 

The data cover the information of the women in 1988 which include the variables of the number of children (children), years of education (educ), age (age), square of age (agesq), living in urban area (urban) and other socio-demographic characteristics. 

(a) Estimate the model 

Children = b0 + b1educ + b2age + b3agesq + b4urban + u

by OLS and present the regress results with essential statistics in the following table.

Dependent variable: children

Independent variable Coefficient Standard error

educ

age

agesq

urban

constant

observations

R-squared

(b) Explain the effect of age on children by interpreting the estimates of β2, and β3. Holding age fixed, what is the estimated effect of another year of education on fertility? If 100 women receive another year of education, how many fewer children are they expected to have?

c) The variable frsthalf is a dummy variable equal to one if the woman was born during the first six months of the year. Assuming that frsthalf uncorrelated with the error term from part (a) and is a potential IV candidate for educ, write down the reduced form for educ. Estimate the reduced form by OLS and show that frsthalf a reasonable IV candidate for educ. (Hint: check the coefficient estimate and 𝑡𝑡-statistic of the IV.)

 

(d) Estimate the model from part (a) by using two-stage least squares with frsthalf  as an IV for educ and present the final results (i.e., the results from the second stage) with essential statistics. Compare the estimated effect of education with the OLS estimate from part (a). 

 

(e) Can you test the exogeneity of the IV by performing the test of overidentifying restrictions? Why or why not?

 

 

Question 2

Use the dataset KIELMCx.DTA for this question. 

(a) The variable dist is the distance from each home to the incinerator site, in feet. Consider the following model: 

log(price)=𝛽0 + 𝛿0𝑦81 + 𝛽1log(dist) + 𝛿1𝑦81 ⋅ log(dist) + u. 

If building the incinerator reduces the value of homes closer to the site, what is the sign of δ1? What does it mean if β1>0? 

 

(b) Estimate the model from part (a) and report the results with essential statistics. Interpret the coefficient on 𝑦81 ⋅ log(dist). What do you conclude about the effect of the incinerator on housing values? 

(c) Explain the partial effect of dist on price in percentage terms. (you don’t need to discuss whether it is significant or not.) 

(d) Add age and agesq to the equation and estimate the model again. Report the results with essential statistics. What do you conclude about the effect of the incinerator on housing values? 

(e) Why the coefficient estimate on 𝑦81 ⋅ log(dist) is statistically significant in part (d) but not in part (b)?

Question 3

Use the dataset JTRAINx.DTA for this question. 

Use the data to determine the effect of the job training grant (grant) on hours of job training per employee (hrsemp). 

The model with the firm fixed effect is as the follows: 

Hrsempit = 𝛽0 + 𝛿1d88t + 𝛿2d89t + 𝛽1grantit + 𝛽2granti,t-1 + 𝛽3log(employit)+ai + uit , 

where d88 and d89 are the dummy variables for 1988 and 1989 respectively, and employ is the number of employees at plant. (In the dataset, lemploy denotes log(employ).) 

(a) Write down the first-differenced equation of equation (1) with an intercept and a time-period dummy. 

(b) Estimate the equation in part (a). How many firms are used in the estimation? How many total observations would be used if each firm had data on all variables for all three time periods? [Note: the first-differenced variables are available in the dataset, you don’t need to generate the variable by yourself.] 

(c) (2 marks) Interpret the coefficient on grant and comment on its significance. 

(d) Is it surprising that grantt-1 is insignificant? Briefly explain your answer.

(e) Do larger firms train their employees more or less, on average? How big are the differences in training?

 

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