Mathematical Modeling of Social Phenomena

Dr. Courtney Brown

Assignment #3

In this assignment, you will analyze the on-year and off-year pattern of political participation in voting during U.S. congressional elections. In on-year elections (every four years), the congressional elections coincide with the presidential elections. More people go out to vote in those elections. In the off-year elections (the elections between the on-year elections), fewer people vote. Thus, congressional electoral mobilization as a proportion of the total eligible voters is greater in on-year elections than in off-year elections due to the structure of the electoral calendar.

You need to do this assignment in two parts. First you need to create a SAS data set, and then you need to analyze the data. You will then conduct your analysis on the data for the years from 1950 to 1970. Use this SAS code to create your data set. Just copy and paste the file into your SAS program editor, change one line, and run it.

Now you need to run a program that analyzes the U.S. congressional elections. Use the program below to do this. Just cut and paste it into your SAS program editor, and then run it.

For your assignment, you are to go through the code below and explain the reason behind using each data statement and proc statement. Look at the output, and then explain the output. What is going on with this program? For example, why are the values of A, B, and Y1 given in the program, and where do those values come from? Why do you need a restrict statement in the regression?

Interpret all of the SAS code and results, and hand it all in together with a nice plot and some tables (for the output). What have you learned about congressional voting and mathematical modeling? Why did I pick the years from 1950 to 1970 for you to conduct your analysis? Why not end in 1972, or 1980? (You need to know a bit about history to answer this.) Why is this relevant to the capabilities of a first-order linear difference equation with constant coefficients?

NOTE: The concept of this interesting assignment was originally developed by Professor John Sprague.

Below is the SAS code that will do the analysis of the data. Cut and paste everything below this line into your SAS editor.

libname windata 'c:\';
GOPTIONS lfactor=10 hsize=6 in vsize=6 in horigin=1 in vorigin=1 in;
options nocenter;
**********************************************************;
* CLASS, NOTE THAT IF YOU BEGIN A LINE WITH AN ASTERISK *
* THEN YOU CAN PUT NOTES IN YOUR PROGRAM FILES. THIS IS
* LIKE A COMMENT CARD IN SPSS. HOWEVER, REMEMBER
* TO EVENTUALLY PUT A FINAL SEMICOLON AT THE END OF YOUR COMMENTS.;
***********************************************************;
* NOTE THAT I INDENT SOME STATEMENTS. THIS
* IS JUST FOR NEATNESS.;
***********************************************************;
* COPYRIGHT (c) Courtney Brown 2004, All Rights Reserved;
* Permission granted to use this file and computer code for any nonprofit and
* educational purposes, including classroom instruction.
* No further permission required.
* Please cite source as "From www.courtneybrown.com";
***********************************************************;
DATA USPARTY;SET windata.USPARTY;
LMTCONG=LAG(MTOTCONG);
IF ((YEAR GE 1950) AND (YEAR LE 1970));
DATA TRAJECT;
A=-1;
B=0.9931;
Y1=0.5714173;
DO YEAR=1950 TO 1970 BY 2;
Y2=(A*Y1)+B;
OUTPUT;
Y1=Y2;
END;
PROC SORT;
BY YEAR;
DATA COMBINE;
MERGE TRAJECT USPARTY;
BY YEAR;
DATA COMBINE;SET COMBINE;
EQUIL=B/(1-A);
PROC PRINT; VAR A B Y1 Y2 EQUIL YEAR MRCONG MDCONG MTOTCONG;
DATA ON;SET COMBINE;
IF ((YEAR EQ 1952) OR (YEAR EQ 1956) OR (YEAR EQ 1960) OR (YEAR EQ 1964) OR (YEAR EQ 1968));
DATA OFF;SET COMBINE;
IF ((YEAR EQ 1950) OR (YEAR EQ 1954) OR (YEAR EQ 1958) OR (YEAR EQ 1962) OR (YEAR EQ 1966) OR (YEAR EQ 1970));
PROC MEANS DATA=ON;
PROC MEANS DATA=OFF;
DATA COMBINE;SET COMBINE;
PROC REG;
MODEL MTOTCONG=LMTCONG;
RESTRICT LMTCONG=-1;
symbol1 color=black v=NONE f=centb i=join;
symbol2 color=black f=centb v='.' height=2 interpol=R;
symbol3 color=black f=centb v='.' height=2;
PROC GPLOT;
axis1 color=black order=0.3 to 0.7 by 0.1
value=(h=1.5 f=swissb c=black)
label=(h=1.3 a=90 r=0 f=swissb c=black 'Congressional Mobilization');
axis2 color=black
value=(h=1.5 f=swissb c=black)
label=(h=1.3 f=swissb c=black 'Year');
PLOT MTOTCONG*YEAR=3 y2*YEAR=1/ overlay
vaxis=axis1 haxis=axis2 vminor=0 hminor=0;
TITLE 'Figure 1: Congressional Mobilization, 1950-70';
run;
quit;