Contract Length: Expected Surplus, Uncertainty, and Speci c Investments

Transcription

1 Contract Length: Expected Surplus, Uncertainty, and Speci c Investments Meng-Chi Tang Michigan State University Job Market Paper Abstract This paper empirically tests how contract length is a ected by expected surplus, uncertainty, and speci c investments. Using the contract information from the National Football League and the franchising industry, I nd that contract length increases with expected surplus and speci c investments. In addition, contract length increases with uncertainty when the seller (player) is more risk averse than the buyer (team), and decreases with uncertainty when the seller (franchisor) is less risk averse than the buyer (franchisee). JEL Classi cations: D86, L2 This is the rst chapter of my dissertation. I am grateful to my advisor, Mike Conlin, for his continuous guidance and support. I also thank Thomas Jeitschko, Je Wooldridge, and Jay Pil Choi for their suggestions, as well as Rob Bond for his expertise on the franchising industry. Financial support from the Department of Economics at Michigan State University is greatly appreciated. All errors are mine. Contact information: Michigan State University, Department of Economics, Marshall-Adams Hall, East Lansing, MI tangmen1@msu.edu 1

2 1 Introduction Why do some contracts have longer duration than other contracts? In an ideal world every contract can be extended to in nity, because every obligation can be speci ed in every conceivable eventuality. However, in a world with unforeseeable contingencies, writing a complete contract is virtually impossible. There are tradeo s associated with longer contracts such as more exibility and less renegotiation cost. The empirical literature testing contract theory provides thin evidence on the determinants of contract length due to the focus on incentive contracts and rm boundaries. 1 Since contract length is one of the most important parameters of nearly every contract, this paper provides evidence on how expected surplus, uncertainty, and speci c investments a ect the length of both commercial and labor contracts. Most of the research on contract length falls into the literature of transaction cost theory, or incomplete contract theory. 2 The central issue is how speci c investments relate to contract length. In particular, Klein, Crawford, and Alchain (1978) argued that if a long-term contract specifying the terms of future transactions can be provided ex ante, the level of opportunistic behavior can be mitigated ex post and thus the speci c investment can be made more e cient. 3 The prediction has been tested in primarily commercial contracts. For example, Joskow (1987) rst tested the prediction using the contracts between coal suppliers and electric utilities. He found that the more important are speci c investments, the longer the contract. Similar evidence is also found in natural gas contracts (Crocker and Masten, 1988), franchise contracts (Brickley, Misra, and Van Horn, 2006, hereafter BMV) and tenancy agreements (Bandiera, 2007), among others. There is minimal research relating expected surplus with contract length. The relationship between expected surplus and contract length is related to the quasi rents mentioned in Klein, Crawford, and Alchain (1978), but di erent in the sense that expected surplus is generated even without speci c investments. Crocker and Masten (1988) empirically tested the relationship using natural gas contracts and found contract length increases with the quasi rents at stake. 1 See Chiappori and Salanié (2003) for a survey on testing contract theory, and Lafontaine and Slade (2007) for a survey on the empirical literature of vertical integration. While the career concerns literature also addresses the problem by relating long-term contracts with the moral hazard problem, it also falls into the literature of incentive contract. For example, see the textbook treatment by Bolton and Dewatripont (2005, p. 470). 2 See Guriev and Kvasov (2005) for a summary of the theoretical literature on contract length and speci c investments, and Shelanski and Klein (1995) for a survey on the empirical literature. 3 Cheung (1969) rst proposed the idea that the tenancy lease duration is chosen to minimize transaction costs, which is de ned as the cost to secure and transfer the right to the income generated by private investment, as well as the renegotiation cost. 2

3 The research relating contract length to uncertainty consist of labor and macroeconomics literature that focuses on how longer contracts trade o the cost of being bounded against the cost of renegotiation. Theoretically, this relationship is ambiguous. While Gray (1978) and Dye (1985) suggest that contract length is negatively related to uncertainty, Harris and Holmstrom (1987) and Danziger (1988) nd that contract length can be positively related to uncertainty. In addition, the empirical literature which uses the union- rm labor contracts also provides mixed evidence. 4 This paper empirically tests the e ects of expected surplus, uncertainty, and speci c investments on contract length, using contract information from the National Football League (NFL) and the franchising industry. The bene ts of using both types of contracts are threefold. First, this allows the possibility to examine whether the determinants of contract length vary across labor and commercial contracts. Second, while the seller (player) is more risk averse than the buyer (team) in the NFL, the seller (franchisor) is less risk averse than the buyer (franchisee) in the franchising industry. Analyzing both contract environments enables the comparison between two contracting environments with di erent relative risk attitudes of the buyer and seller. Third, using both types of contracts enables multiple proxies of expected surplus, uncertainty, and speci c investments to be applied in the empirical test. The paper proceeds as follows. Section 2 lays out a theoretical framework to show how contract length is likely to depend on expected surplus, uncertainty, and speci c investments. Although contract length is found to increase with expected surplus when the risk averse party initially prefers a shorter contract, the model does not provide clear predictions on the e ects of uncertainty and speci c investments. Section 3 proceeds to the empirical analysis and describes the contract information and institutional details of the NFL and the franchising industry. Section 4 discusses the empirical strategy, while Section 5 presents the evidence that contract length increases with expected surplus and speci c investments. In addition, contract length increases with uncertainty when the seller is more risk averse than the buyer in the NFL, and decreases as the seller is less risk averse than the buyer in the franchising industry. Section 6 concludes. 2 A Theoretical Framework Consider a seller and a buyer negotiating a contract to trade a good in a two period model. The buyer and seller can either negotiate a one-period (short) contract or a two-period (long) contract, with price P 1 for the short contract and P L for the long contract. If the buyer and seller negotiate a short contract the rst period, they will negotiate another one-year contract 4 See Wallace (2001) for a brief review on the related literature. 3

4 the second period with price P 2. Before the game starts, the buyer knows his bene t for the good is B 1 in the rst period, but is uncertain about his bene t in the second period, B 2. To be speci c, let B 2 equals B 1 + with probability ; and B 1 with probability 1, where represents the uncertainty in the buyer s bene t. After negotiating the rst contract, the buyer and seller make speci c investments of I B and I S ; respectively. The opportunity cost of the good for the seller is normalized to zero, and the discount factor is assumed to be one. Figure 1 illustrates the timeline of the game. The buyer s payo for a long contract is de ned as EU 2 B = B 1 + EB 2 + (W 0 P L I B ) B ; where W 0 is the initial wealth, and B measures the buyer s risk attitude. The buyer s payo for two short contracts is EU 1 B = B 1 +EB 2 +(W 0 P 1 I B P 2g ) B +(1 )(W0 P 1 I B P 2b ) B ; where P2g and P 2b are the prices for the second short contract if buyer s willingness to pay turns out to be B 1 + and B 1 ; respectively. Since buyer s willingness to pay is higher when P 2g is negotiated, I assume P 2g P 2b : The buyer therefore prefers a long contract if P L < P 1 + P 2b < P 1 + P 2g ; and two short contracts if P L > P 1 + P 2g > P 1 + P 2b : If P 1 + P 2g > P L > P 1 + P 2b ; buyer s preference is uncertain and depends on the probability. The seller s expected utility from a long contract is EUS 2 = (P L I S ) S ; while her expected utility from two short contracts is EUS 1 = (P 1 I S + P 2g ) S + (1 )(P1 I S + P 2b ) S : S indicates the seller s risk attitude. The seller prefers a long contract if P L > P 1 + P 2g > P 1 + P 2b ; and two short contracts if P L < P 1 + P 2b < P 1 + P 2g : If P 1 + P 2b < P L < P 1 + P 2g ; seller s preference is uncertain. Although the choice variables in the model are the prices for long and short contract, I am not solving them explicitly at this stage. Instead, I look at how the buyer and seller s preferences between a long contract and two short contracts change as the parameters change. To simplify the discussion, only two cases are examined in the following discussion: Case 1 highlights a risk neutral buyer and a risk averse seller ( B = 1 and S < 1); while Case 2 highlights a risk averse buyer and a risk neutral seller ( B < 1 and S = 1): For the contract information to be examined later in the paper, Case 1 relates to the contracting environment of the NFL contracts, while Case 2 relates to the franchise contracts. 2.1 Expected Surplus As the expected surplus increases, the buyer or seller will prefer a long contract if their expected payo s from a long contract increase more than two short contracts. Although the price is not explicitly solved, I assume the way to split the surplus from a long contract and two short contracts are the same. L 1 2g 1 2b. Moreover, I also L > 0: 4

5 As shown in the appendix, the buyer and seller prefer a long contract if the risk averse party prefers two short contracts initially. In particular, the long contract will be preferred after buyer s bene t increases if the risk averse seller originally preferred two short contracts in Case 1. In Case 2, the long contract will be selected if the risk averse buyer prefers two short contracts in the beginning. 2.2 Uncertainty If buyer s bene t increases in the second period, I assume the negotiated price for the second short contract is increasing with the uncertainty. > 0: Alternatively, if buyer s bene t decreases in the second period, the negotiated price is assumed to decrease with the uncertainty. < 0: I also assume P L is not a function of. The condition that a long contract will be negotiated after the uncertainty increases is ambiguous, since the preferences of the buyer and seller are di erent in most of the cases, as shown in the appendix. In both Case 1 and Case 2, if the risk neutral party prefers a long contract after the uncertainty increases, the risk averse party will prefer two short contracts. However, if the risk averse party prefers two short contracts, the risk neutral party s preference to contract length is ambiguous. Similarly, if the risk averse party prefers a long contract after the uncertainty increases, the risk neutral party will prefer two short contracts. However, if the risk neutral party prefers two short contracts, the risk averse party s preference to contract length is ambiguous. 2.3 Speci c Investments As mentioned in the introduction, the main nding from literature is that contract length positively relates to speci c investments. In this framework, the party who invests more speci c investments should therefore prefer a long contract. Speci cally, I B as the buyer makes more speci c investments, S investments. S B as the seller makes more speci c When there is greater buyer speci c investment, the appendix shows that the holdup situation is created if the risk averse party prefers a long contract in the beginning of the game. In particular, if the risk averse seller initially prefers a long contract in Case 1, the seller will prefer two short contracts as buyer s speci c investment increases, while the risk neutral buyer prefers a long contract but. Similarly, if the risk averse buyer in Case 2 prefers a long contract initially, the buyer and seller prefer di erent contract length as buyer speci c investment increases. When there is greater seller s speci c investment, the appendix shows that the holdup 5

6 situation is created if the risk averse party prefers two short contracts in the beginning of the game. In particular, if the risk averse seller prefers two short contracts initially in Case 1, the buyer and seller incur the holdup problem as seller s speci c investments increase. Similarly, if the risk averse buyer in Case 2 prefers two short contracts initially, the buyer and seller prefer di erent contract length as seller speci c investment increases. 3 Data and Institutional Details The theoretical framework indicates a relationship between contract length and expected surplus, uncertainty, and speci c investments. Although contract length is found to increase with expected surplus if the risk averse party prefers a shorter contract initially, it is ambiguous to show whether contract will be longer or shorter as uncertainty and speci c investments increase. Now I am going to empirically test these relationships using contract information from the National Football League and franchising industry. 3.1 National Football League Contracts The NFL conducts their annual draft in late April. There are multiple rounds in a draft, and in each round each team owns one pick to select a player. The order of picks is based on the prior year s performance, with the rst pick going to the worst performing team. A team may trade its pick to another team for speci c players and/or picks. After being drafted, the draftee and his agent negotiate a contract with the team. The team has exclusive rights on the draftee which prohibits other NFL teams from signing the player. Almost all draftees agree to contractual terms with the NFL team holding their rights. If a draftee is unable to reach a contractual agreement, he can either sit out a year and reenter the subsequent year s draft or play for another professional football league (such as Canadian Football League). The contract information of those players drafted comes from two time periods, (hereafter 86-91) and (hereafter 01-07). Every contract speci es the duration of the contract and the amount of money payments, which includes signing bonus and base salary. Besides early round draft choices in the drafts, almost all the contracts are not guaranteed in the sense that the team has the right to cut a player and not pay his base salary. Signing bonus, on the other hand, is guaranteed money and paid upfront. Some contracts also include incentive clauses. After the NFL and the NFL Player s Association (NFLPA) entered into a new collective bargaining agreement (CBA) in 1993, the general structure of the contract has become more varied because of the introduction of salary cap. The salary cap limits team s spending on player salaries with signing bonus prorated evenly 6

7 over the duration of the contract. The NFLPA provided the contract data, along with players position, college, selection number in draft, and drafting team. The data include 1,872 contracts from and 1,782 contracts from There were 28 teams having a single pick in each of the 12 rounds from 86-91, and 32 teams having a single pick in each of the 7 rounds from Team information is obtained from the NFL Record and Fact Book ( , ), including team s paid attendance, stadium capacity, win-loss record, and head coach tenure. The population in the metropolitan statistical areas (MSA) is interpolated/extrapolated from the 1990 and 2000 U.S. census. Table 1 presents the summary statistics for each time period. As the table indicates, the average length of the contracts in the dataset is about one year longer than in Contract length ranges between one and six years in the dataset, and one and seven years in the dataset. 6 Figure 2 presents the distribution of contract length for both time periods. In addition, Figure 3 presents the average contract length by round, as well as the proportion of non-division IA school draftees by round. Average contract length decreases across rounds and the rate of the decrease is similar across time periods. The fact that signing bonus is allowed to be prorated evenly over the duration of the contract after imposition of the salary cap is one explanation as to why the average contract length in every round is longer for the data. In addition, the number of non-division IA school draftees increases across rounds for both time periods, while there were more non-division IA school players drafted in the drafts. Summary statistics of the other variables are similar for both time periods, except for the empty seat percentage. The empty seat percentage is much smaller during because attendance has increased approximately 24 percent while there was only a three percent increase in the average stadium capacity. 3.2 Franchise Contracts A franchise contract speci es the agreement between the franchisor and the franchisee on the franchisee s right to use the franchisor s trademark or the right to sell his product in a given place for a speci c duration (Lafontaine, 1992). To test the e ect of expected surplus, uncertainty, and speci c investments on franchise contract duration, I obtained information 5 There were only 31 teams in 2001 because the Houston Texans joined the NFL in The Texan s 12 contracts in 2002 are dropped in the regression analysis since there are no observations for the variables related to the prior year. 6 According to the CBA, players drafted in the rst half of the rst round cannot have their contracts exceed six years, while players drafted in the second half of the rst round cannot exceed ve years. The other draftees contracts length cannot exceed four years. 7

8 from the Bond s Franchise Guide (Bond, 2007), which includes detailed survey responses from 1,005 franchisors. Table 2 presents the summary statistics. 7 The mean duration of the initial contracts is slightly fewer than eleven years; with 51 percent having ten year durations; nineteen percent having ve year durations; and 12 percent having 20 year durations. Table 2 also indicates that ten percent of the franchisors were listed in Bond s Top 100 franchisors (Bond, 2006). 8 In addition, the survey asked each franchisor what building type was allowed for a franchise outlet. Most of the franchisors provided several choices for prospective franchisee, with 21 percent allowing a home-based unit or a kiosk. Figure 4 shows the building types and the proportion of franchisors who allow each building type. Moreover, Table 2 reveals the franchisors have average 20 years of experience in franchising and provide their franchisees an average of 23 days of on- and o -site training. 9 The franchisors have on average 492 units in a chain, where 88 percent of the franchisors units are franchised. Nine percent of the franchisors were in rental, business aid, or educational sectors, and Figure 5 presents the distribution of franchisors by business sector. Finally, many states in the U.S. have statues regulate the franchising industry. Most of these states require good cause for termination and non-renewal of the existing franchising relationship. 10 Table 2 indicates that 33 percent of the franchisors are headquartered in the states restricting termination of a franchise contract. 7 In the survey, a franchisor was asked contact information, background details, required nancial and contract terms of his franchisee, speci c expansion plans in the near future, as well as the support and training provided for his franchisee. Moreover, instead of a single value response, some franchisors responded a range of values for some nancial and contractual variables. In such case the average of the lowest and the highest possible values are used as their responses. Finally, replies that are ambiguous, not applicable, or non-response are treated as missing. 8 Bond s Top 100 franchisors broke the franchising industry into food-services, retail, and service-based franchises, evaluated companies on the basis of historical performance, brand identi cation, market dynamics, franchisee satisfaction, the level of initial training and on-going support, litigation record, and nancial stability, etc (Bond 2006). 9 Franchisors responded to this question using di erent measures, including hours, days, and weeks. All responses are converted into days, where a training day is de ned as a business day (8 hours a day, 5 days a week). Moreover, the o -site training includes training at headquarter, training center, classroom, and current operating unit, while the on-site training indicates training at franchisee s own site. 10 A good cause for termination is the franchisee s failure to comply with the material terms of the franchise contract (Blair and Lafontaine, 2005). 16 states which limit termination for good cause are Arkansas, California, Connecticut, D.C., Delaware, Illinois, Indiana, Iowa, Michigan, Minnesota, Nebraska, New Jersey, Tennessee, Virginia, Washington, and Wisconsin (Klick, Kobayashi, and Ribstein, 2006, Table 4). See also the discussion about contract duration and the termination laws in BMV, footnote 21, and Blair and Lafontaine (2005, p. 279). 8

9 4 Empirical Strategy In this section, I discuss the proxies for expected surplus, uncertainty, and speci c investments from the NFL and franchising datasets. Table 3 compares these proxies for the two types of contracts. 4.1 National Football League Contracts Expected Surplus. Player s selection number and team s number of empty seats and wins last year are proxies for expected surplus. Since the team s bene t for an early draftee is higher than a later draftee, while the player s opportunity cost does not vary by the order of pick, the expected surplus is greater for a team and an early draftee. Moreover, a team with more empty seats and/or fewer wins is willing to pay more for an early draftee to make immediate contribution, compare to a team with fewer empty seats and/or more wins last year. If contract length is positively related to expected surplus, an early draftee s contract from a team with more empty seats and/or fewer wins last year should negotiate a longer contract. Uncertainty. Whether a player attended a Division IA school is a proxy for uncertainty, since the NFL performance of non-division IA draftee is more uncertain. 11 Because the team is less risk averse than the player, contract duration should be greater for draftees that attended non-division IA school. Speci c Investments. Whether a player is quarterback is a proxy for speci c investments. Compared to other positions, a quarterback requires more team-speci c training because he must learn the team s o ensive system and play calling. Since contract length is expected to increase with rm-speci c investment, a quarterback s contract should be longer than the contract for other positions. 4.2 Franchise Contracts Expected Surplus. Whether a franchisor is selected in the Bond s Top 100 franchisors is a proxy for expected surplus. Franchisee s bene t to join the chains of those Top 100 franchisors will likely be higher than other franchisors chains. More expected surplus is therefore generated from contracting with the Top 100 franchisors, since the franchisor s opportunity cost is unlikely to vary across franchisees. Consequently, contract duration for the Top 100 franchisors should be greater. 11 The same uncertainty measure has been used by Hendricks, DeBrock, and Koenker (2003). See footnote 7 in their paper for more discussion on the uncertainty proxy. 9

10 Uncertainty. Since a franchisee is likely more risk averse than the franchisor, contract length is expected to decrease with uncertainty. To measure the risk incurred by franchisee, Lafontaine and Bhattacharyya (1995) used the yearly average proportion of discontinued outlets between 1982 and 1986 in each sector as a measure of risk faced by a prospective franchisee. 12 They found the top three sectors with the highest discontinued outlets during 1982 to 1986 were rental service, business aids, and educational products and services sectors. 13 Accordingly, whether franchisor is in those three business sectors is applied as a proxy for uncertainty. Speci c Investments. Whether a franchisor allows a home-based unit or a kiosk for outlet is a proxy for speci c investments, since the sunk cost of a home-based unit or a kiosk is likely less than the other building types. In addition, the number of required training days is another proxy for speci c investments. Since much of the training is rm-speci c, the more specialized franchisee s skills become, the higher the cost to switch between franchise chains Empirical Results 5.1 National Football League Contracts To test whether contract duration is a ected by expected surplus, uncertainty, and speci c investments, I regress NFL contract length on player s selection number, team s empty seats percentage, team wins the prior year, whether the draftee attended a non-division IA school, as well as the team s MSA population, head coach tenure, prior year s stadium capacity, and whether stadium capacity has increased or decreased by more than 1,000 seats. Team xed e ect, as well as player s position, draft round, and draft year xed e ects are also included in the regression. 15 Binomial regression is applied for the estimation, since contract duration ranges discretely from one to seven. 16 To be speci c, the conditional mean to be estimated is assumed as 12 See Lafontaine and Bhattacharyya (1995) for other risk measures used in the literature. 13 Lafontaine and Bhattacharyya (1995) obtained the data from Franchising in the Economy, published by U.S. Department of Commerce, which is not available after BMV used the amount of o -site training as a proxy for human capital investment. Other than the rm-speci c training, they also emphasized the amount of travel and opportunity cost the franchisee incurs. Since the focus of this paper is investment speci city, the required total training better serves the purpose. Similar empirical results can be obtained if the o -site training is used as the proxy for uncertainty. 15 The empirical results are similar if di erent sets of xed e ects are applied. To be speci c, instead of including all xed e ects in the regression, I have also run the regression with di erent combinations of xed e ects, including 1) draft round only; 2) draft round and player s position; 3) draft round, player s position, and draft year. 16 The other three possible choices for estimation are ordinary least square (OLS), ordered probit regression, 10

11 E(length i jx i ) = p(x i )L where x i denotes the set of regressors; p(x i ) is a logistic distribution; 17 and L is the maximum contract length. Since contract length is restricted, multiplying the estimated probability by L guarantees the tted value will not exceed the sample range. Columns (1) and (4) of Table 4 present the coe cient estimates from this baseline regression. 18 The coe cient estimates support the conjecture that, when the buyer is less risk averse than the seller, contract length increases with expected surplus, uncertainty, and speci c investments. First, the selection number of player has a negative and statistically signi cant coe cient for both time periods. If a player was drafted 20 picks later within a round, the duration of his contract will be reduced by about 0.1 years for both time periods. Notice the coe cient estimates were obtained conditional on the round xed e ects. The round dummy coe cients suggests that, compared to players drafted in other rounds, the rst round draftees obtained an average of 0.57 year longer contract during 86-91, and 2.17 years during The result indicates when there is greater expected surplus from the contracting relationship, team and player signed a longer contract. 19 In addition, the coe cient on empty seats percentage and number of team wins in prior season vary in sign with the only statistically signi cant coe cient being the negative coe cient associated with wins for drafts. 20 Second, players from small schools obtained roughly 0.08 year longer contract than their big school counterparts during 86-91, and 0.04 year longer contract during The coe cient estimates indicate that, when the buyer is less risk averse than the seller, contract length increases with the uncertainty. The result is insigni cant in the and Poisson regression. The problem of OLS estimation is that it may predict the tted value to be more than seven or less than zero. The ordered probit regression is not used since there is no data censoring problem in the contracts used here, which is a common problem in the empirical contract duration literature mentioned by Masten and Saussier (2000). At last, by using Poisson regression, the tted value is assured to be positive but larger than the upper bound of the variable. While only the results from binomial regression are reported, they are robust to these di erent estimation methods. 17 The marginal e ects are similar if the probability function is assumed to be Gaussian. 18 The coe cient estimates reported in Table 4 are not marginal e ects. To calculate the marginal e ect of a continuous variable from the binomial regression, the partial derivative of the probability function with respect to the regressor is evaluated at the sample mean of all regressors. For a dummy variable, the marginal e ect is evaluated as the di erence between the estimated probability when the dummy equals one and when it equals zero. 19 For example, ceteris paribus, if a player was drafted 20 picks later within a round, the duration of his contract will be reduced by about 0.1 years for both time periods. Notice the coe cient estimates were obtained conditional on the round xed e ect is included in the regression. 20 All else equal, one percentage increase of empty seats in the prior year relates to 0.17 year longer contract in the dataset, but 0.38 year shorter contract in the dataset. On the other hand, one more winning game in the prior year relates to year longer contract in the dataset, but year shorter contract in the dataset. 11

12 dataset because there were only nine percent draftees graduated from small schools during 01-07, while 21 percent draftees were from small schools during Third, comparing to other positions, a quarterback had the second shortest contract in the dataset, but the longest one in the dataset. Since players rarely changed teams unless via a trade prior to the 1993 CBA, the holdup issue is more of a concern to the team during Regressions (2) and (5) of Table 4 include an interaction of empty seats and selection number. An interaction of the stadium capacity last year and selection number is also included as a covariate. As discussed in section 4, the e ect of prior year wins and empty seats on contract length may di er for early and late draftees because early draftees are more likely to make an immediate contribution to team performance. The empirical evidence supports this conjecture. All else equal, the empty seats percentage in prior season is positively related to contract length, but the e ect decreases with the selection number. 22 Similarly, regressions (3) and (6) of Table 4 include the interaction term between the number of wins last year and selection number. Compared to other teams, a team with fewer wins last year signed longer contracts with early draftees but shorter contracts with later draftees. 23 These results provide further supports that contract length increases with expected surplus. 5.2 Franchise Contracts To test whether franchise contract length is a ected by expected surplus, uncertainty, and speci c investments, I regress contract length on whether the franchisor was listed in Bond s Top 100 franchisors, whether franchisor allows a home-based unit or a kiosk as an outlet, the number of days of total training, and whether franchisor is in the retail, business aid, or education industry. The other covariates are the number of units in a chain, the number of years since rst franchised, and whether franchisor is headquartered in a state that restricts termination of franchise contract. 24 Since lengths are often much longer for franchise compare to NFL contracts, Poisson 21 For example, the baseline regression indicates a quarterback has an average of 0.13 year longer contract than other positions during By using the same speci cation but excluding the position xed e ect, the regression shows a quarterback has on average 0.05 year shorter contract than other positions during 86-91, but 0.07 year longer contract during For example, compare to other teams in the dataset, longer contracts were signed by the team with more empty seats last year, but the same team signed shorter contracts with the draftees after the 190 th pick. 23 For example, compare to other teams in the dataset, shorter contracts were signed by the team with more wins last year, but the same team signed longer contracts with the draftees after the 185 th pick. 24 BMV applied the number of total units and the number of years since rst franchised as the proxies for learning. They argued franchisor with more experience and units in a chain is able to learn more about the optimal contract terms. The contract length will be longer since the franchisor does not need the exibility to adjust the contract terms. 12

13 regression is an appropriate estimation method. 25 In particular, the conditional mean to be estimated is assumed as E(length i jx i ) = exp(x i ) where x i denotes the set of regressors, and length i given x i has a Poisson distribution. Table 5 presents the coe cient estimates from this speci cation. These estimates are similar whether or not business sector xed e ects are included. The empirical results support the hypothesis that, when the buyer is more risk averse than the seller, contract length increases with greater expected surplus, less uncertainty, and more speci c investments. First, all else equal, franchisors listed in the Bond s Top 100 franchisors provided about 18 percent longer contract than other franchisors, where this di erence is statistically signi cant. The result indicates when there is greater expected surplus from the contracting relationship, franchisor o ered a longer contract. Second, the franchisors in rental, business aid, and education industry provided 42 percent shorter contract than other franchisors. This statistically signi cant coe cient estimate indicates that, when the buyer is more risk averse than the seller, contract length decreases with the uncertainty. Finally, if franchisor allows a home-based unit or a kiosk as a franchise outlet, the franchisor on average provided a 12 percent shorter contract. If a franchisor reduces the required total training by a day, contract length on average shorten by 0.2 percent. These estimates are statistically signi cant and provide the evidence that contract length increases with speci c investments, which is consistent with the literature. 6 Conclusion Among the empirical works on testing contract theory, limited evidence has been found on the determinants of contract length. The existing literature separately examines the e ects of uncertainty on labor contract length and speci c investments on commercial contract length. This is the rst paper to address the relationship between expected surplus and contract length, and tests the determinants of contract length for both commercial and labor contracts using NFL and franchising data. The empirical evidence indicates that contract length increases with expected surplus and speci c investments. In addition, contract length increases with uncertainty when the seller (player) is more risk averse than the buyer (team), and decreases with uncertainty when the seller (franchisor) is less risk averse than the buyer (franchisee). Further research is required to see if these relationships hold for other types of 25 Similar results can be found by using OLS or binomial regressions. 13

14 commercial and labor contracts. Appendix The appendix provides the comparative statistics for section 2. A. Expected Surplus Case 1. As buyer s bene t increases, the risk neutral buyer is indi erent between a long contract and two short contracts 2 B EU 1 B ) = 0. The risk averse seller s preference between a long contract and two short contracts depends 2 S EU 1 S ), which equals S L )[(P L I S ) S 1 (P 1 I S + P 2g ) S 1 (1 )(P 1 I S + P 2b ) S 1 ]: L > 0; the risk averse seller prefers a longer (shorter) contract if she preferred a shorter (longer) contract in the beginning of the game. Case 2. When the buyer s bene t B 2 EU B 1 ) equals B L )[(W 0 P 1 I B P 2g ) B 1 + (1 )(W 0 P 1 I B P 2b ) B 1 (W 0 P L I B ) B 1 ]: L > 0; the risk averse buyer prefers a longer (shorter) contract if she preferred a shorter (longer) contract in the beginning of the game. In addition, the risk neutral seller is indi erent between a long contract and two short contracts 2 S EU 1 S ) = 0. B. Uncertainty Case 1. With the uncertainty increases, the risk neutral buyer s preference depends on the sign B 2 EU B 1 ) ; which equals 2g +(1 2b : The risk averse seller @ depends S 2 EU S 1) ; which equals to s 2g 1 I S + P 2g ) S 1 + (1 2b 1 I S + P 2b ) S 1 ]. The result provides two implications: 1) Assume the risk neutral buyer prefers a long contract as the uncertainty increases, the risk averse seller will prefer two short contracts. However, if the seller prefers two short contracts, the buyer s preference is ambiguous. 2) Assume the risk averse seller prefers a long contract as the uncertainty increases, the risk neutral buyer will prefer two short contracts. However, if the risk neutral buyer prefers two short contracts, the risk averse seller s preference is ambiguous. Case 2. With the uncertainty increases, the risk averse buyer s preference depends on the sign B 2 EU B 1 ), which equals B 2g 0 P 1 I B P 2g ) B 1 + (1 2b 0 P 1 I B P 2b ) B 1 ]: In addition, the risk neutral seller s preference depends S 2 EU S ; which equals 2g + (1 2b. Similar to Case 1, the following two be obtained: 1) Assume the risk neutral seller prefers a long contract as the uncertainty increases, the risk averse buyer will prefer two short contracts. However, if the buyer prefers two short contracts, the seller s preference is ambiguous. 2) Assume the risk averse buyer prefers a long contract as the uncertainty increases, the risk neutral seller will prefer two 14

15 short contracts. However, if the risk neutral seller prefers two short contracts, the risk averse buyer s preference is ambiguous. C. Buyer s Speci c Investments Case 1. If there are more buyer s speci c investments to be made, the risk neutral buyer prefers a long contract 2 S EU 1 S B B : The risk averse seller s preference depends on, which equals S B )(P L I S ) S 1 B )[(P 1 I S + P 2g ) S 1 (1 )(P 1 I S + P 2b ) S 1 ]g: The result indicates that, if the risk averse seller prefers two short contracts or is uncertain about her preference before I B increases, her preference to contract length is uncertain as buyer s speci c investment increases. In addition, if the seller prefers a long contract initially, she will prefer two short contracts as buyer s speci c investment increases. Case 2. If there are more buyer s speci c investments to be made, the risk averse buyer prefers a long contract if B )[(W 0 P 1 I B P 2g ) B 1 +(1 )(W 0 P 1 I B P 2b ) B 1 ] > B )(W 0 P L I B ) B 1 : If the buyer prefers a long contract before she made more speci c investments; her preference to long contract will not be a ected B B. If the buyer prefers two short contracts or is uncertain about her preference in the beginning of the game; it is unclear what contract length the buyer will prefer as her speci c investments increase. In addition, the risk neutral seller prefers two short contracts B D. Seller s Speci c Investments B : Case 1. If there are more seller s speci c investments to make, the risk averse seller prefers a long contract if S )(P L I S ) S 1 > S )[(P 1 I S +P 2g ) S 1 +(1 )(P 1 I S +P 2b ) S 1 ]: If the seller originally prefers two short contracts, she will prefer a long contract as her speci c investments increase S S. However, if the seller prefers a long contract or is uncertain about her preference in the beginning of the game, it is unclear what contract length the seller will prefer as her speci c investments increase. In addition, the risk neutral buyer prefers a long contract S S. Case 2. If there are more seller s speci c investments to make, the risk neutral seller prefers a long contract S S : The risk averse buyer s preference depends 2 EU B 1 S, which equals B S )[(W 0 P 1 I B P 2g ) B 1 + (1 )(W 0 P 1 I B P 2b ) B 1 ] S )(W 0 P L I B ) B 1 g: If the buyer originally prefers two short contracts, she will prefer a long contract as seller s speci c investments increase. However, if the buyer prefers a long contract or is uncertain about her preference in the beginning of the game, it is unclear what contract length the buyer will prefer as seller s speci c investments increase. 15

16 References [1] Bandiera, Oriana. "Contract Duration and Investment Incentives: Evidence from Land Tenancy Agreements," Journal of the European Economic Association, 2007, 5(5), pp [2] Blair, Rogert D. and Lafontaine, Francine. The Economics of Franchising, 2005, Cambridge University Press. [3] Bolton, Patrick and Dewatripont, Mathias. Contract Theory, 2005, The MIT Press. [4] Bond, Robert E., et al. Bond s Franchise Guide, 2007, Source Book Publications. [5]. Bond s Top 100 Franchises, 2006, Source Book Publications. [6] Brickley, James A.; Misra Sanjog; and Van Horn, R. Lawrence. "Contract Duration: Evidence from Franchising," The Journal of Law and Economics, 2006, 49(1), pp [7] Cheung, Steven N.S. "Transaction Costs, Risk Aversion, and the Choice of Contractual Arrangements," The Journal of Law and Economics, 1969, 12(1), pp [8] Chiappori, Pierre-André and Salanié; Bernard. "Testing Contract Theory: a Survey of Some Recent Work," CESifo Working Paper Series No. 738, 2002, SSRN: [9] Crocker, Keith J. and Masten, Scott E. "Mitigating Contractual Hazards: Unilateral Options and Contract Length," RAND Journal of Economics, 1988, 19(3), pp [10] Danziger, Leif. Real Shocks, E cient Risk Sharing, and the Duration of Labor Contracts, Quarterly Journal of Economics, 1988, 103(2), pp [11] Dye, Ronald. "Optimal Length of Labor Contracts," International Economic Review, 1985, 26(1), pp [12] Gray, Jo A. "On Indexation and Contract Length," Journal of Political Economy, 1978, 86(1), pp [13] Guriev, Sergei and Kvasov, Dmitriy. "Contracting on Time," American Economic Review, 2005, 95(5), pp

17 [14] Harris, Milton and Holmstrom, Bengt. "On the Duration of Agreements," International Economic Review, 1987, 28(2), pp [15] Hendricks, Wallace; DeBrock, Lawrence and Koenker, Roger. "Uncertainty, Hiring, and Subsequent Performance: The NFL Draft," Journal of Labor Economics, 2003, 21(4), pp [16] Joskow, Paul L. "Contract Duration and Relationship-Speci c Investments: Empirical Evidence from Coal Markets," American Economic Review, 1987, 77(1), pp [17] Klein, Benjamin; Crawford, Robert G. and Alchian, Armen A. "Vertical Integration, Appropriable Rents, and the Competitive Contracting Process," The Journal of Law and Economics, 1978, 21(2), pp [18] Klick, Jonathan.; Kobayashi, Bruce H. and Ribstein, Larry E. "The E ect of Contract Regulation: The Case of Franchising," George Mason Law & Economics Research Paper No , SSRN: [19] Lafontaine, Francine. "Agency Theory and Franchising: Some Empirical Results," RAND Journal of Economics, 1992, 23(2), pp [20]. and Bhattacharyya, Sugato. "The Role of Risk in Franchising," Journal of Corporate Finance, 1995, 2, [21]. and Slade, Margaret. "Vertical Integration and Firm Boundaries: The Evidence," Journal of Economic Literature, 2007, 45(3), pp [22] Masten, Scott E. and Saussier, Stephane. "Econometrics of Contracts: An Assessment of Developments in the Empirical Literature on Contracting," Revue d Economie Industrielle, 2000, 92, pp [23] Vázquez, Luis. "Determinants of Contract Length in Franchise Contracts," Economics Letters, 2007, 97, pp [24] Wallace, Frederick H. "The E ects of Shock Size and Type on Labor-Contract Duration," Journal of Labor Economics, 2001, 19(3), pp

18 Table 1 Summary statistics of the NFL contracts during and Variable Contract length (0.80) (1.02) Proportion of division IA player (0.41) (0.28) Empty seat ratio last year (0.14) (0.08) Average paid attendance last year per home game (10,000 seats) (0.92) (0.80) Capacity last year (10,000 seats) (0.92) (0.61) Dummy=1 if stadium capacity increased more than 1,000 seats from the prior year (0.25) (0.27) Dummy=1 if stadium capacity decreased more than 1,000 seats from the prior year (0.15) (0.20) Wins last year a (2.96) (3.05) Head coach tenure (6.38) (3.05) Metropolitan population (1,000,000) (4.94) (4.95) Observations a Note: a. Variables related to the prior year have sample size equals Standard errors in parentheses

19 Table 2 Summary statistics of the franchise contracts information from Bond (2007) Variables Mean Length of the initial contract (in year) (6.46) Dummy=1 if listed as Top 100 franchisors in (0.30) Dummy=1 if allowed building type of unit are home-based or kiosk 0.21 (0.41) Years since first franchised (12.58) Number of days of required total training (25.65) Number of total units (in 1,000) 0.49 (1.98) Dummy=1 if the franchisor is in rental, business aid, or education sectors 0.09 (0.28) Dummy=1 if headquartered in the state restricts the termination of franchisee 0.33 (0.47) Observations 1005 a Note: a. Sample size varies across variables since some franchisors did not respond to every question in the survey. Standard errors in parentheses

20 Table 3 Proxies for expected surplus, uncertainty, and specific investments in the NFL and the franchise contracts Contract Expected surplus Uncertainty Specific Investments NFL *Selection number in the draft *Whether player graduated from *Whether player is a quarterback *Percentage of empty seats Division IA school *Team wins prior year Franchise *Whether franchisor is listed *Whether franchisor is in rental, *Whether allowable building type for as a Top 100 franchisor business aid, and education sectors outlet includes home-based or kiosk *Number of days of total training

21 Table 4 Binomial regressions: Dependent variables (Contract length of the NFL contracts) Independent Variables (1) (2) (3) (4) (5) (6) Selection number in the draft *** ** *** * ** (0.001) (0.002) (0.002) (0.001) (0.002) (0.001) Empty seats percentage in home games last year ** (0.132) (0.166) (0.132) (0.185) (0.286) (0.183) Empty seats percentage in home game last year* *** *** selection number in the draft (0.001) (0.002) Number of team wins last year * ** *** (0.005) (0.005) (0.007) (0.004) (0.004) (0.008) Number of team wins last year prior to draft* 0.055* 0.157*** selection number in the draft divided by 1,000 (0.029) (0.044) Dummy=1 if graduated from Division IA school *** *** *** (0.019) (0.019) (0.019) (0.031) (0.031) (0.031) Dummy=1 if player is quarterback a ** 0.095** 0.084* (0.049) (0.048) (0.048) (0.047) (0.046) (0.046) Metropolitan population (1,000,000 person) *** *** *** (0.054) (0.055) (0.054) (0.033) (0.033) (0.033) Number of head coach tenure at draft year 0.013*** 0.013*** 0.013*** (0.003) (0.003) (0.003) (0.004) (0.004) (0.004) Stadium capacity of team last year (10,000 seats) (0.044) (0.046) (0.044) (0.037) (0.049) (0.036) Stadium capacity of team last year (10,000 seats)* selection number in the draft divided by 1,000 (0.090) (0.235) Dummy=1 if stadium capacity increased *** *** *** more than 1,000 seats from the prior year (0.049) (0.048) (0.049) (0.032) (0.032) (0.032) Dummy=1 if stadium capacity reduced * * * more than 1,000 seats from last year (0.058) (0.057) (0.058) (0.039) (0.039) (0.039) Indicator variables, including draft round, player s position, draft year, and draft team fixed effects YES YES YES YES YES YES Observations R-squared b Log-likelihood Note: a. The coefficients were estimated relatively to the position of defensive linebacker. b. R-squared is the squared correlation coefficient between the observed and the fitted values of the contract length variable. The coefficient estimates are not marginal effects. Robust standard errors presented in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%.