**
POLS 6482 ADVANCED MULTIVARIATE STATISTICS
Fifth Assignment
Due 8 October 2001**

- The aim of this problem is to learn how do coefficient tests
in
**EVIEWS**and**STATA**using the Refrigerator data discussed in Epple Notes IV pp.15-19. Download the data and bring it up in**EVIEWS**.

Refrigerator Data

- Replicate the analyses performed in Epple Notes IV pp.15-19.

- Answer questions 4.3 and 4.4 on page IV-22. With respect to question 4.4,
generate an appropriate variable in
**EVIEWS**and run the regression.

- Paste the dataset into
**STATA**, insert the appropriate names and labels, do the**d**and**summ**commands and report the results.

- In
**STATA**run the regression shown on page IV-15.

- In
**STATA**perform the Wald Test discussed on page IV-19:

**test Opcost=-9.385**

- Replicate the analyses performed in Epple Notes IV pp.15-19.
- This problem is a continuation of 1.c of the 3
^{rd}homework and 2 of the 4^{th}homework. I made some corrections in the file so download the new version:

105th Elections Data by Congressional District (HDMG105Y.DTA)

- Bring up the HDMG105Y.DTA in
**STATA**. Do the**d**and**summ**commands and report the results.

Note that there are three types of variables: personal characteristics of the representative (e.g.,**female**,**aamer**,**himem**,**rep**,**catholic**, etc.); demographics of the congressional district (e.g.,**black**,**hisp**,**asian**, etc.); and election results (e.g.,**clint96**,**dole96**,**bush92**, etc.).

The variable**dwnom1**is a measure of the economic liberalism/conservatism of the member of Congress and it ranges from approximately -1 (liberal) to +1 (conservative). The variable**dwnom2**is a measure of the social liberalism/conservatism of the member of Congress and it ranges from approximately -1 (social-liberal) to +1 (social-conservative).

- Paste HDMG105Y.DTA into
**EVIEWS**. Run the regression:

**ls clint96 c black south hisp income dwnom1 dwnom2 female aamer himem**

Do the results make sense to you? Specifically, should the personal characteristics of the representative have any effect upon the Clinton vote in the congressional district? Justify your answer.

- If we believe that the personal characteristics of the member of the House should
have no effect upon the presidential vote, then this is tantamount to testing the following
null hypothesis:

**b**_{female}= b_{aamer}= b_{himem}= 0

We can test this null hypothesis using the method discussed in Epple Notes V. The method is a more elaborate version of the simple Wald test done on the refrigerator data. Follow the same steps discussed on page IV-19. For example, if the variable**female**is**C(3)**in the Estimation Equation and**aamer**and**himem**are**C(4)**and**C(5)**respectively, in the Estimation Equation, then the command in**EVIEWS**is

**WALD C(3)=C(4)=C(5)=0**

**(WARNING! Note that WALD C(3)=C(4)=C(5) tests whether or not the coefficients***have the same value*! This is different from testing whether or not they all are equal to zero!)

- In
**STATA**, to perform the Wald test first run the regression and then type:

**test female aamer himem**

This tests**b**_{female}= b_{aamer}= b_{himem}= 0

An alternative way to perform the test that sometimes is very convenient is to first type:

**test female=0**

then type:

**test aamer=0, accumulate**

This tests**b**. Then if you type:_{female}= b_{aamer}= 0

**test himem=0, accumulate**

You get the full test**b**. The keyword "accumulate" causes_{female}= b_{aamer}= b_{himem}= 0**STATA**to test the joint restriction that the coefficients on**female**, then**aamer**, and then**himem**are all equal to zero.

**(Note that, to test b**_{female}= b_{aamer}= b_{himem}you would use the commands:

test female=aamer

then:

test female=himem, accumulate)

- In
**EVIEWS**run the above regression without the personal characteristics of the representative; namely:

**ls clint96 c black south hisp income dwnom1 dwnom2**

The sum of squared error should befor this regression (**larger****Sum squared resid**in the**EVIEWS**regression table). How much larger is it? Compute the difference and divide by 3 ("3" is the number of restrictions -- see Epple notes V pp.1-7 -- the formula is**(SSE**). This number is the numerator of the formula shown in Epple notes V-1. Now, take the sum of squared error from the full regression with the personal characteristics (this is_{R}- SSE_{UR})/number of restrictions**SSE**in Epple notes V) and divide it by 425. This is the denominator of the formula shown in Epple notes V-1. Compute the resulting number and compare it to the value shown in the Wald tests (show all of your work). The two numbers should be the same. This is the F-Statistic for the Wald test._{UR}

- Take the above result and calculate the P-Value using
**EVIEWS**. Suppose the F value is .55. In**EVIEWS**enter the command:

**scalar pval=@fdist(.55,3,425)**

"pval" will now appear in the**EVIEWS**workfile. Double-Click on "pval" and the probability, .648389482496, will appear at the bottom of the window. The "3,425" in the fdist argument gives the degrees of freedom for the numerator and denominator, respectively.

To calculate the P-Value using**STATA**enter the command:

**display fprob(3,425,.55)**

and the probability, .64838948, will appear in the "**Stata**Results" window.

- Bring up the HDMG105Y.DTA in