# This question is an extension of Exercise 10.22. Consider the data file (m r o z) on

## Question:

This question is an extension of Exercise 10.22. Consider the data file \(m r o z\) on working wives and the model \(\ln (W A G E)=\beta_{1}+\beta_{2} E D U C+\beta_{3} E X P E R+e\). Use the 428 observations on married women who participate in the labor force. Let the instrumental variable be MOTHEREDUC.

**a.** Write down in algebraic form the three moment conditions, like (10.16), that would lead to the IV/2SLS estimates of the model above.

**b.** Calculate the IV/2SLS estimates and residuals, \(\hat{e}_{I V}\). What is the sum of the IV residuals? What is \(\sum\) MOTHEREDUC \(_{i} \times \hat{e}_{I V, i}\) ? What is \(\sum E X P E R_{i} \times \hat{e}_{I V, i}\) ? Relate these results to the moment conditions in (a).

**c.** What is \(\sum E D U C_{i} \times \hat{e}_{I V, i}\) ? What is the sum of squared IV residuals? How do these two results compare with the corresponding OLS results in Exercise 10.22(b)?

**d.** Calculate the IV/2SLS fitted values FLWAGE \(=\hat{\beta}_{1}+\hat{\beta}_{2} E D U C+\hat{\beta}_{3} E X P E R\). What is the sample average of the fitted values? What is the sample average of \(\ln (W A G E), \overline{\ln (W A G E)}\) ?

**e.** Find each of the following:

Compute \(S S R_{-} I V+S S E_{-} I V, R_{I V, 1}^{2}=S S R_{-} I V / S S T\), and \(R_{I V, 2}^{2}=1-S S E_{-} I V / S S T\). How do these values compare to those in Exercise 10.22(d)?

**f.** Does your IV/2SLS software report an \(R^{2}\) value. Is it either of the ones in (e)? Explain why the usual concept of \(R^{2}\) fails to hold for IV/2SLS estimation.

**Data From Exercise 10.22:-**

Consider the data file mroz on working wives and the model \(\ln (W A G E)=\beta_{1}+\beta_{2} E D U C+\) \(\beta_{3} E X P E R+e\). Use the 428 observations on married women who participate in the labor force.

**a.** Write down in algebraic form the three moment conditions, like (10.13) and (10.14), that would lead to the OLS estimates of the model above.

**b.** Calculate the OLS estimates and residuals, \(\hat{e}_{i}\). What is the sum of the least squares residuals? What is the sum of squared least squares residuals? What is \(\sum E D U C_{i} \times \hat{e}_{i}\) ? What is \(\sum E X P E R_{i} \times \hat{e}_{i}\) ? Relate these results to the moment conditions in (a).

**c.** Calculate the fitted values \(\widehat{\ln (W A G E)}=b_{1}+b_{2} E D U C+b_{3} E X P E R\). What is the sample average of the fitted values? What is the sample average of \(\ln (W A G E), \overline{\ln (W A G E)}\) ?

**d.** Find each of the following:

Compute \(S S R+S S E, R^{2}=S S R / S S T\) and \(R^{2}=1-S S E / S S T\). Explain what these calculations show about measuring goodness-of-fit.

**Data From Equation 10.13 and 10.14:-**

## Step by Step Answer:

**Related Book For**

## Principles Of Econometrics

**ISBN:** 9781118452271

5th Edition

**Authors:** R Carter Hill, William E Griffiths, Guay C Lim