This assignment is due at the beginning of class. Papers turned in at the end of the class will have a 10% percent penalty. No papers will be accepted after class.
As before, form a team of no more than three people and submit a paper jointly. However, each of you should do the exercise and then compare notes. If you divide it up, you will not learn the methodology very well. Also, be very careful in carrying out the steps. Remember the cliche "garbage in, garbage out." If you screw up, then start over again. The computer session doesn't take that long once you understand what is going on. If you need help, we are here. But you have do your part first. Bring relevant printouts. Also copy all the files saved in the user directory and bring it so that we can troubleshoot.
You will be using Data4-11 in this computer assignment (see Page 646 for a description of this data set). The dependent variable will be HOUSING (new building permits authorized) and the rest of the list will be the independent variables.
1. If you haven't already done so, download the latest version of GRETL.
Click GRETL
to download the new version to your personal computer. Click the
gretl for Windows link and gretl_intall.exe for the program
and data files and the link to manual.pdf for the complete manual. Choose any location in
the
2. Run GRETL, and select FILE, OPEN DATA, SAMPLE FILE, data4-11 and click OPEN. You will get a list of variables. Highlight the variables from density to statetax by holding the left mouse key down and dragging (housing should be excluded here). Next click DATA from the menu at the top, CORRELATION MATRIX, and SELECTED VARIABLES. You will see a matrix of pairwise correlation coefficients on the screen. Minimize this window for now.
3. From the menu in the top row, select MODEL and OLS procedure. Click housing and CHOOSE. Also click SET AS DEFAULT. This will set housing as the dependent variable for all the models you estimate.
4. From the list of variables, select density and click DENSITY and ADD. Repeat this procedure for each of the other independent variables. Note that the constant term is already included. When done, click OK to get OLS estimates for the "kitchen sink" model (omitting the t-subscript and using b's for betas)
5. Study the screen output for Model 1 and identify the variable that has the least significant coefficient. NEVER SELECT THE CONSTANT TERM TO OMIT. The next step is to omit this variable from the model. To do this, select from the menu list in the top row, TESTS and OMIT VARIABLES. From the list of available independent variables, click the name of the one you just chose and then SELECT. Press OK to estimate Model 2. You will note that a single * appears in the last column of the table of coefficients for one of the independent variables. This implies that the corresponding coefficient is significant at a level between 5 and 10 percent. Two *s mean significance at a level between 1 and 5 percent. Three *s mean significance at levels below 1 percent. The more stars you see, the better the strength of significance.
6. Repeat Step 5 and omit variables one by one until you find that all the coefficients have at least one * except for the constant, which you should never pay any attention to.
7. Close all windows and exit from the program. When asked about saving the commands from the session and results, say YES and choose HW2out as the output file name. The steps you took will be translated to command lines and the file HW2out.gretl will have them. The output of all the screens will be in the text file HW2out.txt.
8. Use MSWORD to read the file HW2out.txt. Highlight the whole file and change font to COURIER NEW size 10. Also set the left and right margins to 1". If you don't make these changes, the columns will not line up properly. Then save the file and print it.
9. Submit the computer printout of HW2out.txt. In it, write down why you omitted the particular variable in each step. Don't just say that "it was least significant". Explain technically what drew you to that conclusion.
10. Attach a report in which you explain what sign you expect for each coefficient in the general Model 1 and why. Do the observed signs agree with your intuition? In the result for the correlation matrix see if there is evidence of multicollinearity. Explain what this might have done to the results of Model 1 and how subsequent models support your conclusion.
11. Designate Model 1 as Model U (unrestricted) and the last model you estimated as Model R (restricted). Suppose you want to use these two models to test whether a few coefficients are jointly significant or not. State the null hypothesis for this in terms of the b's (that is betas) and the alternative hypothesis. Next carry out the appropriate joint test using information from Models U and R. What do you conclude?