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45-734 Probability and Statistics II
(4th 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 105th). 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
personal beliefs and not the interests of her district. This is called
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:
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!
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
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
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"
value (for example, .05, .10) and then run
a regression using only those variables with p-values less than
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
Y = the absolute value of the ideological shift of a representative from
Congress t-1 to Congress t.
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
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,
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
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
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.