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This is the second part of the series on Instrumental Variables. For other parts of the series follow the tag instrumental variables.

In this exercise set we will build on the example from part-1.

We will now consider an over-identified case i.e. we have multiple IVs for an endogenous variable. We will also look at tests for endogeneity and over-identifying restrictions.

Answers to the exercises are available here.

**Exercise 1**

Load the AER package (package description: here). Next, load `PSID1976`

dataset provided with the AER package. This has data regarding labor force participation of married women.

Define a new data-frame that has data for all married women that were employed. This data-frame will be used for the following exercises.

**Exercise 2**

We will use a more elaborate model as compared to the previous set.

Regress `log(wage)`

on `education`

, `experience`

and `experience^2`

.

**Exercise 3**

Previously, we identified `feducation`

and `meducation`

as possible IVs for `education`

.

Regress `education`

on `experience`

, `experience^2`

, `feducation`

and `meducation`

. Comment on your results.

**Exercise 4**

Test the hypothesis that `feducation`

and `meducation`

are jointly equal to zero.

**Exercise 5**

Use 2SLS to estimate the IV based return to education.

**Exercise 6**

Use the `ivreg`

command to get the same results as in Exercise-5. Note that standard errors would be different.

**Exercise 7**

There is a short form for the `ivreg`

command which saves time when we are dealing with numerous variables.

Try the short format and check that you get the same results as in Exercise-6.

**Exercise 8**

Regress `log(wage)`

on `education`

, `experience`

, `experience^2`

and residuals from the model estimated in Exercise-3.

Use your result to test for the endogeneity of `education`

.

**Exercise 9**

Regress the residuals from exercise-7 on `experience`

, `experience^2`

, `feducation`

and `meducation`

.

Use your result to test for over-identifying restrictions.

**Exercise 10**

The two tests we did in exercises 8 and 9 can be conveniently obtained using the `summary`

command with diagnostics turned on. Verify that you get the same test results with the `summary`

command.

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