Problem Set 5 Solved

 Question 1 - Price Elasticity of Demand for Air Travel (60 points)

Use the data in AIRFARE.DTA for this exercise. We are interested in estimating the price elasticity of air travel demand. The main variables in the data set are: passen: average passengers per day.

f are: average airfare.

dist: the route distance (in miles).


    1) (15 points) Estimate the price elasticity of air travel demand using OLS, controlling for the year speci c e ects (year dummies) and the route distance (ldist and ldistsq). What is the estimated price elasticity of air travel demand (Interpret the sign and magnitude of the coe cient)? Based on your estimation results what is the average change in demand for air travel from year 1997 to 2000?

    2) (15 points) Estimate the same model in question (1) using xed e ects (FE) model. What is the estimated price elasticity of air travel demand? Explain why you are not able to estimate the e ect of route distance on air travel demand with FE approach. Discuss which approach is preferable for the correct estimation of price elasticity parameter (FE or OLS)? Explain your answer.

    3) (10 points) Since there might be a simultaneity bias in the estimation of price elasticity, we decide to use an instrumental variable (IV) approach. Consider the variable concen, which is a measure of market concentration. (Speci cally, it is the share of business accounted for by the largest carrier.) Explain in words what we must assume to treat concen as a valid IV. Check whether concen satis es the relevance assumption.

    4) (20 points) Now, using the concen as an IV, estimate the demand function using Two Stage Least Squares (2SLS) estimator (you are expected to implement the two step estimation procedure as we discussed in the class.). What is the estimated price elasticity of demand? Next, estimate the same model using "ivreg" command in STATA. What is the main di erence as compared to your previous 2SLS results?

Question 2 - Education and Fertility (40 points)

The data in FERTIL2.DTA include, for women in Botswana during 1988, information on number of children, years of education, age, and religious and economic status variables.

1) (10 points) Estimate the model




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children =  0 +  1educ +  2age +  3age2 + u;

by OLS, and interpret the estimates. In particular, holding age xed, what is the estimated e ect of another year of education on fertility? If 100 women receive another year of education, how many fewer children are they expected to have?

2) (10 points) The variable f rsthalf is a dummy variable equal to one if the woman was born during the rst six months of the year. Assuming that f rsthalf is uncorrelated with the error term from part (1), show that f rsthalf is a reasonable IV candidate for educ. (Hint: You need to do a regression.)

    3) (10 points) Estimate the model from part (1) by using f rsthalf as an IV for educ. Compare the estimated e ect of education with the OLS estimate from part (1).

    4) (10 points) Add the binary variables electric, tv, and bicycle to the model and assume these are exogenous. Estimate the equation by OLS and 2SLS and compare the estimated coe cients on educ. Interpret the coe cient on tv and explain why television ownership has a negative e ect on fertility.



































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