45-734 Probability and Statistics II (4th Mini AY 1997-98 Flex-Mode and Flex-Time) Assignment 4

45-734 Probability and Statistics II (4^th Mini AY 1997-98 Flex-Mode and Flex-Time)

Assignment #4: Due 16 April 1998

In a Republic the supreme power rests in the body of citizens entitled to vote and this power is exercised by representatives chosen directly or indirectly by the citizenry. In theory, a Republic arises from the fact that the citizens are too numerous to be gathered in one place to make decisions. From the larger number a smaller number must be chosen and given the power to make decisions. How the small number should decide is the question of representation. Edmund Burke, a philosopher and a member of the British Parliament in the latter part of the 18th Century, stated the problem in its (now) classic form. Burke outlined two possible types of representatives. A Delegate is a representative who strives to determine what the people want and then votes that way in Parliament. A Trustee is a representative who votes for what is in the "best interests" of the people regardless of what the people think.

We are going to perform a (partial) test of this distinction between a delegate and a trustee using data from the U.S. House of Representatives for the 1947 - 1984 period. Members of the House are elected for two year terms (i.e, one Congress, the current Congress is the 105^th). Our dependent variable is a measure of the change in roll call voting patterns by House members from one Congress to the next (a roll call is a recorded vote -- every member must either vote "yes" or "no" on a parliamentary motion). Loosely speaking, our dependent variable can be thought of as measuring the ideological shift by a member from one Congress to the next. Since what we wish to study is the shift and not its direction, our dependent variable is the absolute value of the shift.

If a member is a delegate, then that member should have a very stable voting record. That is, she will ascertain the interests of her constituents on all issues of importance and then always vote the same position whenever those issues arise (for example, if her district consists mostly of farms, she will always vote for the economic interests of farmers). However, suppose she believes that subsidizing farmers is not good economics but votes for it anyway because she desires to be re-elected. Now, after 10 terms (20 years) in the House, she announces that she will be retiring at the end of the current Congress and will not run for re-election. Will her voting pattern now change?

Economists, using the principal-agent theory applied to representation, say that, yes, her voting pattern will change. She will vote according to her personal beliefs and not the interests of her district. This is called shirking.

However, suppose instead that she grew up on a farm and owns a farm herself. Now her personal interests coincide with those she represents. Will her voting pattern change in these circumstances?

What we are going to test is whether or not members -- once they know they are not going to serve in the next Congress -- change their voting patterns in the current Congress (that is, they exit at the end of Congress t so they do not serve in Congress t+1; did their voting pattern change from Congress t-1 to Congress t?). What we wish to study is whether or not ideological shifts vary systematically between those who remain in the House and those who leave. We are going to use a number of indicator variables (see the attached description of the variables) to control for a wide variety of reasons why members exit other than voluntary retirement (for example, death in office, losing office in an election, and so on). Our dataset:

House.wf1

is a pooled cross-sectional time series. Consequently, we have to control for "fixed effects" -- that is, uniform effects that may increase the mean shift from one Congress to the next (these are the indicator variables, D1 - D18).

First, run the overall regression with all 26 independent variables. Note that, for every observation, D1 through D18 sum to one! Consequently, if you use C (LS Y C D1 D2 D3 ........) you will fall into the "dummy variable trap" (EVIEWS will send you an error message that you have a "near singular matrix"). Run the overall regression omitting C! Now, run the overall regression using C but omitting one of D1 through D18 (turn in both outputs). Why are the coefficients on the variables other than D1 through D18 unchanged? Now try running the regression with just D1 through D18 (note this is simply doing an analysis of variance -- see Epple Note Set VIII). Test whether or not the omitted 8 variables are jointly significant (turn in the output).

Now, try running the regression omitting the fixed effect indicators (D1 - D18). Should you use an intercept term in this situation? Test whether or not the omitted 18 fixed effect indicators are jointly significant (turn in the output). Interpret the signs on the coefficients of the 8 variables. Do they make sense in terms of the theory outlined above (ignore the p-values for the time being)?

Returning to the full model (using D1 - D18 with C omitted) using all 26 variables, select a "reasonable" a value (for example, .05, .10) and then run a regression using only those variables with p-values less than a. Test whether or not the omitted variables are statistically significant (turn in the output). Use this process to arrive at what you think is the best model given these variables -- that is, the model which you think best combines parsimony and explanatory power. Interpret the signs on the coefficients of the variables in your preferred model -- do they make sense?

Finally, investigate the relationship between NOTVOTE and the remaining independent variables other than D1 - D18. In particular, run a regression with NOTVOTE as the dependent variable and the 7 other variables as independent variables. (Be sure to use C here!) Interpret the signs of the coefficients -- do they make sense? (Turn in your output.)

Overall, what do you think this tells you about the nature of representation in the U.S.?

Description of Variables
Sample Size = 6288

Dependent Variable: Y = the absolute value of the ideological shift of a representative from Congress t-1 to Congress t.

Independent Variables:

       Fixed Effect Variables
D1 through D18 are indicator (dummy) variables for the Congress pairs 80-81, 81-82, ... , 97-98. If a representative was in the 80th and 81st House of Representatives, then D1=1; otherwise D1=0. The remaining indicators are similarly defined. These variables control for uniform effects that may increase the shift for all members.

       Exit Variables
APPOINT is an indicator (dummy) variable for appointment to higher office (e.g., the President's Cabinet, state supreme court judge, etc.). If the representative was appointed, then APPOINT=1, otherwise APPOINT=0.
DIED is an indicator (dummy) variable for death in office. If the representative died in office, then DIED=1, otherwise DIED=0.
HIRUN is an indicator (dummy) variable for a retirement in order to run for a higher office (e.g., Senate, state governor, president). If a representative ran for higher office, then HIRUN=1, otherwise HIRUN=0.
LOST is an indicator (dummy) variable for losing either a primary or general election. If the representative was defeated in his/her party primary or in the general election, LOST=1, otherwise LOST=0.
RETIRE is an indicator (dummy) variable for voluntary retirement. If the representative retired in Congress t then RETIRE=1, otherwise RETIRE=0.

       Other Variables
NOTVOTE is the sum of the fractions of roll calls on which the representative did not vote in Congresses t-1 and t. This variable is necessary to control for early exits. For example, if a representative dies in office, then she votes less. Because the accuracy of the ideological measure is based upon the number of votes cast by the representative, clearly dying early in the Congress will result in less precision in the estimation and therefore the representative may appear to shift. This variable is included to control for this type of effect.
REDIST is an indicator (dummy) variable for whether or not the representative's district was re-districted (that is, the geographic boundaries were changed) between Congress t-1 and Congress t. If the geographic boundaries are changed -- for example, a district that was entirely rural now has its boundaries changed to include a city -- then the representative's constituency changes. Hence, a representative may shift her ideological position in response to the change in constituency.
VOTESHR is the representative's share (as a fraction) of the two party vote in the election for Congress t-1. This variable is included to check whether or not a representative is altering her voting pattern in response to her election margin in the previous election. For example, perhaps if she won her previous election by a margin of only 52% to 48%, she may shift her voting patterns to try to increase her margin in the election in time t.

Note that Y, NOTVOTE, and VOTESHR are continuous variables while the remaining variables are indicator (dummy) variables.