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Quantitative Methods II

Problem Set 2

When using STATA for portions of this assignment: Make sure to hand in 1) a print out of a do-file containing all the commands that you used; and 2) written answers to the questions.  Each question is worth 2 points unless stated otherwise (20 pts total).

Exercise 1  Cigarette smoking and birth weight.

The key variables we will focus on in the study are as follows:

 – birth weight of a child (in lbs)

 – number of cigarettes smoked

 – dummy variable for white

 – mother’s education

 – father’s education

 – log of family income

 – taxes on cigarettes (in cents)

 – price of cigarettes (in cents).

a) We want to estimate the effect of  on  while controlling for , , and .  Discuss one potential reason that could prevent us from using OLS to estimate a causal effect of cigarettes smoked on birth weight.  

b) You decide to try and address this potential endogeneity by using an instrumental variables approach, with  and  used as instruments for .  State the two conditions necessary to use an IV estimation.  Without looking at the subsequent results, explain whether you think the two conditions hold here.

c) Now you run the first stage regression and obtain the following results:

Discuss what the above results imply for your instrumental variables estimation.

d) Next you obtain the fitted values  from the above regression and obtain the following second stage results

Can you derive a causal claim from this regression result?  Explain your answer.

Exercise 2  Proof of lack of consistency of SEM using simple OLS

Consider the SEM for price and quantity given by the following two equations

Define the corresponding reduced form equations as follows:

a. Using linear algebra applied to the two structural equations of the SEM, derive a simple expression for  in terms of .

b. Show that the first structural equation does not satisfy consistency.  Hint:  Begin with , substitute the relevant reduced form equation for , and then simplify.

Exercise 3  Relationship between starting wage and subsequent income.  

The data set contains the following variables:  

 – log monthly wage (in Thai baht)

 – log monthly starting wage (in baht)

 – experience at current job

 – years of education

 – dummy variable for males

 – experience at previous jobs

a) First, we begin by running a regression of on , , , and

Is the coefficient on statistically significant?  Provide an economic interpretation of this coefficient.

b) You decide to see if a Simultaneous Equations Model (SEM) can help you obtain a causal effect.  The model you choose to estimate is the following.  

Is the  coefficient identified in the above model (Yes or No)?

Explain why the above model helps you identify the  coefficient.

c) You want to obtain the fitted value for  from the first stage regression.  List the variables you would use as regressors in the first stage regression (no need for explanation).

d) You obtain the fitted value for  and use it in the following second stage regression.  Is the coefficient on  statistically significantly different from 0 at the 5 percent level?  Is it significantly different from the answer obtained from the linear regression in a)?