Measuring Efficiency in the Presence of Head-to-Head Competition Thomas R. Sexton, Ph.D., College of Business, Stony Brook University Herbert F. Lewis, Ph.D., Department of Technology and Society, Stony Brook University

Background Political campaign finance reform has received much attention in recent years. The Bipartisan Campaign Reform Act of 2002 (McCain-Feingold Act) placed new limits on who can contribute, and how much they can contribute, to political campaigns. Campaign managers must pay greater attention to the efficiency with which campaign funds are spent. 2

The Traditional DEA Model The traditional Data Envelopment Analysis (DEA) model, which measures the relative efficiency of operational units that consume multiple inputs to produce multiple outputs, is not well suited for this challenge. Fails to incorporate the head-to-head nature of political campaigns in which a candidate spends money not only to increase the number of votes he or she receives but also to reduce the number of votes that his or her opponents receive. 3

Head-to-Head Competition Head-to-head competition is common in sports. ◦ Zak et al. (1979), Mazur (1994), Anderson and Sharp (1997), Sueyoshi et al. (1999), Lozano et al. (2002), Haas (2003), Fried et al. (2004), and Cooper et al. (in press). ◦ However, none of these explicitly incorporates the head-to-head nature of individual contests. ◦ Sexton and Lewis (2003), and Lewis and Sexton (2004a, 2004b) apply DEA to baseball and formulate models in which a team uses its resources both to score runs and to inhibit their opponents from doing the same. ◦ However, their models analyze season-long data rather than individual contests. 4

Our Paper: Political Campaigns We present a new DEA model that explicitly incorporates the head-to-head nature of political campaigns. We apply the model to the U.S. Congressional races in New York State in 2002, 2004, and ◦ We identify races in which the loser would have won had he or she been efficient. ◦ We identify incumbents as being particularly wasteful in their campaign spending. ◦ We explore how campaign efficiency and the aggregate amount of wasteful spending have evolved over this period. 5

Earlier Studies Earlier studies have addressed the topic of whether spending by an incumbent or a challenger is more efficient. ◦ Jacobson (1978) and Abramowitz (1988) claim that spending by a challenger is more efficient and produces larger gains than does spending by an incumbent. ◦ Others argue that campaign spending by incumbents and challengers are both efficient while still others think that neither incumbent spending nor challenger spending is efficient (Levitt 1994, Gerber 1998, and Erikson and Palfrey 2000). See also Palda (1996), Gerber (2004), Mangee (2002), Palda (2002), Goodliffe (2004), and Primo (2004). 6

DEA Methodology Linear programming-based methodology first introduced by Charnes, Cooper, and Rhodes (1978). DEA is an extreme point method that compares each producer with only the “best” producers. It has been applied in many fields: criminal justice (Lewin et al. 1982), electricity production (Fare and Primont 1984 and Norton et al. 2002), public financing for school bus transportation (Sexton et al. 1994), retail store management (Anderson 1996), campaign financing (Coates 1999), and blood centers (Pitocco and Sexton 2005). 7

The DEA Approach Collection of DMUs, each of which consumes multiple inputs to produce multiple outputs. Allows for site characteristics: factors that affect efficiency but lie beyond control of the DMU. Establishes the efficient frontier based on the observed best performance among all DMUs. Evaluates the efficiency of each DMU relative to this frontier. The best producers lie on the efficient frontier and can be used as a reference set for the inefficient DMUs that do not lie on the frontier. 8

Campaign DEA Model Consider an election in which there are n t candidates competing in period t. ◦ We exclude candidates who are unopposed, those who spend less than $5000, and those who receive no votes in the general election. Let x jt = money spent by Candidate j and x' jt = total money spent by all of Candidate j’s opponents combined. Let y jt = number of votes cast for Candidate j and let y' jt = total number of votes cast for all of Candidate j’s opponents combined. 9

One Candidate 10 Candidate j Candidate j’s Opponent(s) x jt x' jt y jt y' jt

Standardized Spending and Votes 11 Candidate j Candidate j’s Opponent(s)

Candidate Status Define three binary variables: ◦ Let I jt = 1 if Candidate j is an incumbent, with I jt = 0 otherwise. ◦ Let C jt = 1 if Candidate j is a challenger, with C jt = 0 otherwise. ◦ Let S jt = 1 if Candidate j is running for an open seat, with S jt = 0 otherwise. We consider candidate status to be a site characteristic. 12

13 Maximize target’s vote differential Target spends less money Target’s opponents spend more Target gets more votes Target’s opponents get fewer votes Variable returns to scales Target has same status Nonnegativity subject to

Target Spending and Votes 14

Three Efficiency Measures : Own spending : Own votes : Opponents’ votes 15

If All x j Were Equal Candidate A

If All x j Were Equal Candidate B

If All x j Were Equal Candidate C

Data We obtained data on votes received and on campaign spending from the Federal Election Commission web site ( We chose to analyze the congressional districts in New York State because they are designed to each incorporate, as closely as possible, precisely the same population. In addition, New York has a large number of congressional districts (29) and candidates, which is desirable in any DEA model. 19

Candidates and Races 20 YearCandidates Two-Way Races Three- Way Races All118534

Efficient Candidates 21 YearCandidates Efficiency Measure Own Spending Own Votes Opponents’ Votes * (57.5%) 18 (45.0%) 10 (25.0%) (67.4%) 23 (50.0%) 19 (41.3%) (78.1%) 17 (53.1%) 16 (50.0%) All (66.9%) 58 (49.2%) 45 (38.1%) * P-value = in a chi-square test.

The Consequences of Inefficiency In 6 of the 57 races (10.5%), a losing candidate would have won had he or she been efficient. In each case, the losing candidate’s target candidate would have been a winner, would have spent less money than the losing candidate, and would have faced an opponent who spent more than the losing candidate’s opponent did. One of the six was a challenger, two were incumbents, and three were running for an open seat. 22

Election Outcome Reversals 23 YearCDCandidateEXEX θyθy E y’ ActualIf Loser Efficient SpendingVotesSpendingVotes Bishop (O)1.000 $958,54580,886$958,54549,408 Grucci (O) $1,399,76878,465$739,23478, Bishop (I)1.000 $1,908,440156,354$1,923,967153,723 Manger (C) $1,367,904121,855$1,367,904162, Higgins (O)1.000 $1,332,162143,332$1,332,162118,792 Naples (O) $1,581,433139,558$1,204,117139, Hall (C)1.000 $1,602,865100,119$1,602,86567,445 Kelly (I) $2,519,16495,359$2,316,985125, Arcuri (O)1.000 $2,192,558109,686$2,192,55882,485 Meier (O) $1,586,39791,504$1,586,39793, Kuhl (I)1.000 $1,475,375106,077$2,351,01898,845 Massa (C) $1,445,525100,044$1,445,525101,725

Savings and Vote Increases 24 Year Total SpendingTotal Votes CandidatesActual If All Efficient % Reduction * Actual If All Efficient % Increase $20,316,640$9,546, %2,722,2053,335, % $32,501,954$23,742, %5,002,3155,877, % $40,392,018$35,687, %2,799,5573,119, % All118$93,210,612$68,975, %10,524,07712,332, % * P-value = in Kruskal-Wallis one-way nonparametric ANOVA.

Spending and Votes per Candidate 25 Year Spending per Candidate Votes Received per Candidate Actual If All Efficient Actual If All Efficient 2002$507,916$238,66068,05583, $706,564$516,133108,746127, $1,262,251$1,115,23187,48697,487 All$789,920$584,54189,187104,512

Spending per Vote Received 26 Year Spending per Vote Received Actual If All Efficient % Reduction * 2002$7.46$ % 2004$6.50$ % 2006$14.43$ % All$8.86$ % * P-Value = in Kruskal-Wallis one-way nonparametric ANOVA.

Incumbents Much Less Likely to be Efficient Spenders 27 E x = 1E x < 1Total% E x = 1 * Incumbents % Challengers % Open Seat % All % * P-value < in a chi-square test.

Conclusions About two-thirds of Congressional candidates in NYS in 2002, 2004, and 2006 spent campaign funds efficiently. However, about half could have received more votes and more than 60% could have kept more votes away from their opponents. Campaigns spend more, but more efficiently. ◦ Campaign spending per candidate and spending per vote roughly doubled from 2002 to ◦ Inefficiency accounted for more than half of campaign funding in 2002 but only about 10% in

Conclusions More than 10% of losing candidates would have won had they been efficient. Effect of inefficiency is dominated by incumbency status. ◦ Challengers and candidates running for an open seat are much more likely to be efficient in their spending. ◦ Yet incumbents won over 96% of elections. ◦ One possible explanation is that incumbents are likely to have more money on hand. ◦ Given the limited uses for campaign funds, incumbents have little choice but to spend the money on campaign activities. 29