Franchise values in North American professional sports leagues: evidence from the repeat sales method.

Humphreys, Brad R. ; Lee, Yang Seung

Introduction

Accurate measurement of the value of professional sport franchises is important to our understanding of the operation of sports leagues. Fort (2006) pointed out two important features of sport franchise values: First, the lack of audited financial data from professional sports teams in North America, coupled with incessant, hard to verify, claims of financial difficulties made by team owners places a premium on the analysis of observable data like actual prices paid for professional sports teams on the open market; second, franchise values increased dramatically over the past 100 years, outstripping the growth rate of the overall economy by a wide margin, and understanding why franchise values grew so rapidly is an important research question in sport finance. Even if the underlying flows of revenues cannot be observed, finance theory indicates that the price paid for an asset that generates a stream of revenues over time should reflect the present discounted value of the underlying flow of net revenues. Claims of losses often play an important role in team owner's requests for public subsidies for facility construction and operation, further heightening the importance of accurate measurement of franchise valuation.

Previous research on the value of sports franchises in North America used two approaches: unconditional analysis of transaction prices and hedonic models applied to franchise values. The unconditional analysis of franchise sale prices and estimates of franchise values focuses on describing changes in these values over time. The hedonic approach has been widely used to analyze the factors affecting the value of a number of assets including houses, art (Goetzman 1993; Beggs & Gaddy, 2006), vintage wine (Burton & Jacobsen, 2001), and antique furniture (Graesner, 1993), in addition to sports franchises. The hedonic method provides a theoretical grounding for the analysis of franchise prices, controls for changes in the quality of the franchise, and generates estimates of the hedonic price of observable characteristics of franchises that provide important information about the factors that drive changes in franchise values. In this paper, we use two alternative approaches, the repeat sales method and a hybrid model that includes both repeat sales and single transactions, to analyze actual franchise sale prices over the period 1960-2009 in the National Football League (NFL), National Basketball Association (NBA), National Hockey League (NHL), and Major League Baseball (MLB). Both methods generate quality adjusted price indexes for franchise values that represent the average market price of a generic sports franchise. The quality adjusted price index for the repeat sales model assumes no change in franchise quality over time; the index for the hybrid model allows for observable characteristics related to quality to change, but uses different assumptions than hedonic models. In addition, the hybrid model makes use of all transactions, while the repeat sales model only uses observations for which multiple transactions occurred.

Quigly (1995) proposed an extension to the repeat sales model, a hybrid model, to address efficiency and bias problems occurring in repeat sales and hedonic models. We use this hybrid model developed by Quigley as an alternative to the more restrictive repeat sale model. This model is appropriate for this setting because the error structure includes unmeasured characteristics related to quality, and measuring quality of sports franchises is difficult. The error structure in Quigley's model is more general than other competing models, so the estimator should be more efficient. We discuss this model in detail below.

Fort (2006) performed an unconditional analysis of both actual franchise sale prices and annual estimates of franchise values published in Financial World and Forbes magazines over the past few decades. Fort concluded that owning a professional sports team in North America was a profitable experience over the past hundred years, since the average increase in franchise sale prices exceeded the growth rate of the aggregate economy over the same period.

The hedonic approach uses a model relating estimated franchise values to observable characteristics of the teams and the markets they play in to explain observed variation in the franchise value. Alexander and Kern (2004) estimated a hedonic model that included income in the local market, population of the local market, team success as measured by finish in the previous season's final standings, an indicator for teams with a regional orientation, an indicator variable for teams that relocated from another location, and an indicator variable for the presence of a new stadium as observable characteristics using data on annual estimated franchise values in the National Football League (NFL), National Basketball Association (NBA), National Hockey League (NHL), and Major League Baseball (MLB). Income and population in the local market had positive hedonic prices, as did higher finishes in the final standings and new facilities.

Miller (2007) estimated a hedonic model using panel data from MLB over the period 1990-2002. Hedonic characteristics included market income and population, current and lagged winning percentage, an indicator variable for privately owned stadiums, the age of the team's facility, the age of the team and the team's tenure in its current home. Market population, but not market income, current and past success, and playing in private stadiums all had positive hedonic prices; stadium age had a negative hedonic price, suggesting a reason why teams frequently seek public subsidies for new stadium construction projects. Miller (2009) estimated a hedonic franchise value model using panel data from the NFL, NBA, and NHL over the period 1991-2004. This paper used the same set of hedonic characteristics as in Miller (2007). Market income, but not population, lagged success, but not current success, and playing in a privately owned facility had positive hedonic prices; facility age had a negative hedonic price.

Although Alexander and Kern (2004) and Miller (2007, 2009) do not examine increases in franchise values, these papers identify a set of observable franchise characteristics that affect estimated franchise values, providing important information for understanding increases in franchise values over time. These three studies used estimated franchise values developed by Financial World and Forbes magazines instead of transaction prices. Fort (2006) observed that the estimated franchise values were often quite different from actual sales prices, so the hedonic prices estimated in these three studies could reflect problems estimating the value of sports franchises and not actual changes in the actual value of the underlying asset, a professional sports team. Humphreys and Mondello (2008) estimated a hedonic franchise value model using transactions panel data from the NFL, NBA, MLB, and NHL over the period 19692006. Hedonic characteristics included market population, franchise and facility age, an indicator variable for private facility ownership, success over the past five years, and the number of competing professional sports teams in the local market. Population, franchise age, and private ownership of the facility had positive hedonic prices; competing professional teams in the local market had a negative hedonic price. Humphreys and Mondello (2008) constructed a quality adjusted franchise price index from the empirical results; this index showed a clear upward trend beginning in the early 1980s, indicating that changes in observable factors related to franchise value were not driving observed increases in franchise values over the past three decades and confirming Fort's (2006) finding of significant returns to professional sports team ownership. Differences in estimated hedonic prices in this study can be attributed to the use of actual transaction prices instead of estimated annual franchise values.

All of the conditional analyses discussed above use a similar empirical approach that can be interpreted in terms of a standard hedonic model: explain the observed variation in franchise values or transaction prices using observed variation in observable characteristics of the franchises, the markets they play in, and the facilities they play in. Hedonic models have a number of well-documented limitations in this setting (Meese & Wallace, 1997). First, theory provides no guidance on the functional form of the hedonic model, leading to the possibility of specification bias affecting the results. Miller (2007, 2009) demonstrates that the estimated hedonic prices on private ownership and facility age exhibits sensitivity to model specification, suggesting that the specification of the hedonic model may be important in this setting. Second, the ability of the hedonic model to explain variation in franchise values depends on the availability of observable variables that capture the quality of the franchise. Professional sports teams generate many unobservable and intangible benefits, including the public goods effects like the generation of "world class city" status on the host community, a sense of community and commonality among fans and other residents of the host city (Johnson & Whitehead, 2000), and other difficult to quantify factors related to the perceived quality of the franchise related to reputation. In the hedonic models discussed above, these unobservable team-specific quality attributes are captured by team-specific intercept terms.

The Repeat Sales Method

The repeat sales method represents an alternative approach to hedonic models for analyzing changes in sports franchise values. Repeat sales methods use the change in franchise sales prices from one sale to the next to account for the hedonic characteristics of franchise prices. The use of changes in sales prices removes the effect of unobservable time-invariant hedonic characteristics; it also avoids any econometric problems associated with specification of the hedonic model and lack of data capturing hedonic characteristics. Following the approach in the real estate literature, we assume that a North American market for professional sports franchises exists, and that the sale price of a sports franchise in this market arises from a stochastic process where the average rate of change, sometimes called the price drift in this literature, can be represented by a market index and the dispersion of franchise values around this average market rate of change in a log diffusion process. Let Pit be the price paid for sports franchise i in year t. Given these assumptions, the log of franchise prices can be expressed

ln([P.sub.it]) = [[beta].sub.t] + [H.sub.it] + [N.sub.it] (1)

where [[beta].sub.t] is a market franchise price index, [H.sub.it] is a Gaussian random walk term, and [N.sub.it] is a mean zero, constant variance random variable, so that [N.sub.it] ~ (0, [[sigma].sup.2.sub.N]). The Gaussian random walk term captures variation in individual franchise value growth rates around the market growth rate. The mean zero random variable captures cross-sectional variation in franchise values due to completely idiosyncratic differences in franchises at each point in time during the sample. These factors are assumed to be uncorrelated over time. If franchise prices evolve in this way, then the total percentage change in price for a given franchise i that is purchased at time s and again at time t can be expressed as

[[DELTA]V.sub.it] = ln([P.sub.it]) - ln([P.sub.is])

= [[beta].sub.t] - [[beta].sub.s] + [H.sub.it] - [H.sub.is] + [N.sub.it] - [N.sub.is] (2)

The properties of this stochastic process are

E[[H.sub.it] - [H.sub.is]] = 0

E[[([H.sub.it] - [H.sub.is]).sup.2]] = [A.sub.t-s] + [B.sup.2.sub.t-s]

E[[N.sub.it]] = 0

E[[H.sub.it][N.sub.js]] = 0

E[[N.sup.2.sub.it]] = C

where A, B, and C are parameters defining the variance of the stochastic process over time. Note that the second equation incorporates the assumption that the variance of this stochastic process increases at an increasing rate as time between sales increases. Given a sample of repeat sales of sports franchises over time, the difference in the natural log of the franchise values of franchise i that is sold multiple times in the sample period can be expressed

[DELTA][V.sub.i] = [summation]ln([P.sub.i]) [D.sub.i] (3)

where [D.sub.i] is an indicator variable equal to 1 if period [tau] is the time of the subsequent observed sale, equal to -1 if period [tau] is the time of the previous observed sale, and equal to zero in other periods. Using equation (1), equation (3) can be expressed

[DELTA][V.sub.i] = [summation][[beta].sub.[tau]][D.sub.i[tau]] + [[epsilon].sub.i] (4)

where the [[beta].sub.[tau]]'s are unknown parameters to be estimated. The estimated [[beta].sub.[tau]]'s can be used to calculate an index number for sports franchise values holding quality constant. The index can be calculated by

[I.sub.t] = 100[e.sup.[beta]t] (5)

Note if the variance parameters A and B are not equal to zero, Case and Shiller (1989) showed the variance of the equation error term in (4) is heteroscedastic and proposed a feasible Generalized Least Squares (GLS) estimator to correct for this problem. The GLS estimator is based on the fact sports franchise i that is sold in periods s and t in the sample has a predicted sale value of

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Consequently, the predicted price is the actual price marked up by the expected market appreciation. Based on the assumed functional form of the variance structure described above, the deviation of the actual franchise price from its expected value is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and A, B, and C can be estimated using the residuals of (4) as the dependent variable from the above equation. The fitted values from this can be used to transform the original observations of [DELTA][V.sub.i] and correct for the heteroscedasticity.

The Hybrid Method

Quigley (1995) suggested a hybrid model to analyze housing prices by combining both single sales and multiple sales. We apply his methodology to franchise valuation. In this hybrid approach, franchise value can be represented by a multiplicative term, PQ, where P is a price index of sports franchises and Q is the innate quality of each franchise. We can represent the relationship as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1')

Here, [V.sub.it] denotes the franchise value and can be defined as the sum of the logarithm of the observed price and the franchise quality. [Q.sub.it] captures the quality of franchise i sold at time t, and Pt is the logarithm of the price index at time t. [[epsilon].sub.it] is a random error.

According to equation (1'), each franchise has some level of quality [Q.sub.it], at price [P.sub.t] at time t. The unobservable quality [Q.sub.it] can be estimated using some observable characteristics [Y.sub.it] of traded franchises and franchise-specific factors [[psi].sub.i]. That is, the unobservable franchise quality [Q.sub.it] can be represented as a function of [Y.sub.it] and [[psi].sub.i] as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2')

Substituting (2') into (1) gives

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3')

Let [[phi].sub.it] be a composite error term, so that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4')

where [mu]it = [[theta].sub.it] + [[epsilon].sub.it]. Assume that the relationship between these unobservable error terms is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5')

Finally, suppose that franchise prices follow a random walk such that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6')

Recall from above that, if the variance parameters A and B are not equal to zero, Case and Shiller (1989) showed the variance of the error term ([[mu].sub.it]) is heteroscedastic and proposed a feasible Generalized Least Squares (GLS) estimator to correct for this problem. The intuition behind equation (6) is that the estimate of A determines whether the variance is linear with the elapsed time between the previous sale and the subsequent sale. That is, the variance of franchise prices increases (decreases) with elapsed time if A has a positive (negative) estimated sign. The estimate of B determines the curvature of the variance as a function of elapsed time. If B is positive (negative), then the variance increases at an increasing (decreasing) rate over time.

To find the efficient estimates of the parameters of the hybrid model, using single and multiple sales data, we can combine equations (3') and (4'). The new error structure is a composite error term [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as defined before. This gives the hybrid model

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7')

The unknown parameters of this equation can be estimated2using a sample of both single and repeat sales. We can easily estimate the variances, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. That is, after estimating the parameters of (7') using a subsample of repeat sales, we can obtain an estimate of the variance, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Similarly, after estimating the parameters of (3'), we can obtain an estimate of the variance, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The main difference between these two regression models is that the first regression model includes a set of dummy variables that represent unobservable franchise characteristics while the second regression does not. In equation (7'), [[psi].sub.i] captures the random factors that affect individual franchise values. Intuitively, if we have some information about franchise-specific factors then the random error can be identified through the regression model, much like the fixed effects in standard panel data models. We use indicator variables for new teams, teams in new locations, teams that own their own facility, and variables reflecting the number of competing teams and leagues in the market to control for franchise quality and proxy for [[psi].sub.i].

After obtaining estimates of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], an unbiased estimator [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be found with some manipulation. Details can be found in Quigley(1995). As discussed before, the sample of multiple sales yields the estimates of A and B from equation (6").

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6")

Using the estimates [??] and [??], the variance-covariance matrix of disturbances can be found from Equation (7') as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8')

Intuitively, when i = j, the sample of single sales has estimated variance [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. However, if the sample of multiple sales is included, the estimated variance is increased by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. When [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] since we assume that all errors are independent. From equation (8'), the GLS weights can be derived like those in the repeat sales model, using

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where M is the number of franchises and f corrects for degrees of freedom, i.e., f = (N - M)/N, where N is the degrees of freedom needed to compute [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Equation (7') can be estimated by GLS using the entire sample of single sales and multiple sales. Using all observations, including single sales and multiple sales, increases the efficiency of estimation of the parameters [alpha] and thus estimates of [P.sub.t] can also be improved. The presence of unobservable attributes related to quality was a problem in the repeat sales model. In the hybrid model, the unmeasured attributes actually contribute to explaining the total variance for the model, using all observations. The hybrid model relaxes the assumption that unobserved quality remains constant and uses a method similar to the repeat sales method described above.

Data Description

The data source on franchise sale prices is Rodney Fort's Sports Business Data website (http://www.rodneyfort.com/PHSportsEcon/Common/OtherData/DataDirectory.ht ml). This web site contains franchise sales price data for all four of the major North American professional sports leagues--the NBA, NFL, NHL, and MLB--back to the early part of the 20th century. We analyze franchise sale prices over the period 1960-2009. We restricted our sample to the post-1960 period because the quality of franchises must remain constant for the repeat sales method to work and the longer the time period analyzed the less likely is this assumption to hold. Many of the franchise sales are fractional--an individual or group of investors buys a portion of a professional sports franchise. Following the method used by Fort (2006), we converted all fractional sales to full value. For example, if 50% of a franchise was sold for $10 million dollars, we estimate the total franchise value at $20 million dollars.

The data set contains observations for all franchise sales in the four major North American professional sports leagues over the period 1960-2009. There were 275 individual franchise sales during the sample period in these four leagues; 80 occurred in MLB, 77 in the NBA, 56 in the NFL, and 62 in the NHL.

Table 1 contains summary statistics on the franchise sales over the sample period, in current dollar or nominal terms. Research on the sale price of real estate, art, and other assets uses nominal prices rather than real prices to avoid bias introduced by deflation; this also makes the results comparable to the nominal rate of return on other assets like stocks and bonds. We follow this convention in this paper. From Table 1, NFL franchises had the largest average sale price and NHL franchises the smallest. NBA sale prices were more volatile than other leagues and NHL sale prices were the least variable. The largest price paid for a sports franchise in the sample was $2.125 billion dollars paid for the New York Knicks in 1997. While this transaction would appear as an outlier initially, closer examination revealed this transaction also included Madison Square Garden, an extremely valuable piece of real estate in midtown Manhattan. The largest price paid for an NFL franchise was $1.2 billion dollars paid for the Miami Dolphins in 2009. That transaction included Dolphins Stadium. The largest price paid for a MLB franchise was $889.5 million paid for the Chicago Cubs in 2009. That transaction included Wrigley Field. The largest price paid for an NHL franchise was $575 million paid for the Montreal Canadians in 2009. That transaction included the Bell Centre. Ownership of the team's stadium or arena had a significant effect on the sale price, consistent with the results in Miller (2007, 2009).

Implementing the Case-Shiller estimator requires repeated observations on the sale of the underlying asset. In this case, we need observations on repeated sales of the same sports franchises in order to estimate a quality-adjusted sport franchise appreciation. Fortunately, the 1960-2006 time period contains a number of repeat sales of sports franchises. Of the 275 franchise sales occurring from 1960 to 2009, 139 were repeat sales of a sports team, although none of these repeat sales took place until 1967. These repeat sales involved about 50 teams and among the franchises with multiple sales, the average number of transactions was 3. Most of the repeat sales involved only two transactions; however, the Boston Celtics were bought and sold six times during this period and the Philadelphia Eagles and Minnesota Vikings were bought and sold five times. There is at least one transaction in every year in the sample except 1971, 1976, 1979, and 1987.

The repeat sales in the sample period are summarized in Table 2. Baseball teams appear most frequently and football teams appear least frequently in this sample of repeat sales. The % change variable is the average value for the variable [DELTA][V.sub.it] from the previous section; it is the difference in the log of the sale price from period t to period s. This value approximates the percentage change in the sale price calculated by the traditional formula. The average number of years between sales in the sample, t-s, was 10 years, with a standard deviation of 7.6. The longest period between transactions was 35 years. Owners of sports teams realized a considerable gain when they sold their team; the average rate of return was well over 100% in all leagues, and the extreme figures confirm several owners realized gains in the neighborhood of 300%.

The negative minimum values reported on Table 2 deserve some explanation, as negative returns to owning a professional sports team would appear unlikely. Only eight of the transactions in the sample generated a loss and virtually all of those can be explained as anomalous. The largest negative return in the sample, a 68% loss, involved the sale of 80% of the Chicago White Sox to Bill Veeck in the 1970s. The second largest negative return in the sample, a 61% loss, was the sale of the Pittsburgh Penguins in 1975. The franchise was in bankruptcy at the time, for the second time in five years, and had been taken over by the league. The other negative returns on Table 2 represent fractional purchases of additional stakes in teams by the same individual. The -41% return for MLB comes from the 1973 sale of a 7% stake in the Cleveland Indians by Nick Mileti. Mileti bought the Tribe in 1972 for $10.8 million and sold a 7% interest in the team the next year for $500,000. The -40% return in the NBA is from the 1972 sale of the Boston Celtics. Transnational Communications, a holding company owned by businessman E. E. Erdman, bought the Celtics for $6 million in 1970 and sold the team to Bob Schmertz for $4 million in 1972.

Results and Discussion

The Repeat Sales Model

The repeat sales data described in the previous section was used to estimate a quality-adjusted sports team sale price index implementing the Case-Shiller three-step estimation procedure outlined by Case and Shiller (1989) and described above. The three-step procedure is a feasible Generalized Least Squares (GLS) estimator controlling for quality differences by using only repeat sales data. The first stage involves regressing the log first difference of the franchise sales price on a vector of year dummy variables. The second stage uses the squared residuals from the first stage as the dependent variable and the number of years between sales, and the square of this value, as explanatory variables. The third stage dependent variable is the log first difference of the sale price from the first stage divided by the square root of the fitted value from the second stage in order to correct for heteroscedasticity. The results of this estimation procedure are available by request.

The key summary statistic for the repeat sales model is the quality adjusted price index that can be calculated from the parameter estimates for equation (4) using the 141 repeat sales of professional sports franchises from 1967 to 2009. Most of the parameters are statistically significant at conventional levels and our model explains almost 70% of the observed variation in growth of franchise values from sale to sale. Figure 1 contains a time series plot of the quality-adjusted sports franchise price index that can be calculated from these parameter estimates using equation (5). Because there are relatively few repeat transactions early in the sample period, some of the early index values may not be well identified. The quality adjusted index values are identified by multiple transactions that take place in each year. Some early years in the sample have only one transaction, which means that the parameters from those years may not be precisely estimated.

Recall this price index holds the underlying quality of sports franchises, including factors like market characteristics, team reputation, and league characteristics constant. Several interesting features are apparent in Figure 1. The index exhibits quite a bit of variability. The year-to-year variation in the index can be substantial, involving changes of several hundred points in the index value. This variation can be attributed to the relatively small sample size. The average number of repeat sales transactions in a year in the sample is 0.957. In addition, an extreme value occurs in 2001, where the index value equals 1277. This extreme value contributes to the high year-to-year variation. Three repeat transactions took place in 2001. The Atlanta Hawks (price $184 million) were sold for the first time since 1977, the Montreal Canadians (price $228 million) were sold for the first time since 1971, and the Seattle SuperSonics (price $200 million) were sold for the first time since 1984. The franchise prices were not extraordinary relative to other sales in the early 2000s, but these three franchises had not changed hands in decades, so the change in the price was exceptionally large for each transaction. Meese and Wallace (1997) point out the sensitivity of repeat sales and hedonic models to these types of outliers. We view this value as an outlier attributable to coincidental circumstances.

[FIGURE 1 OMITTED]

There is no apparent upward trend in the index. The average value of the index over the past four decades is 162.7 in the 1970s, 424.7 in the 1980s, 328.2 in the 1990s, and 380.8 in the 2000s. The dashed line on Figure 1 is a quadratic time trend drawn through the sample. This trend line peaks at some point in the early 1990s.

The Hybrid Model

We use the same data as in the analysis of the repeat sales model and all single sales that were dropped for the repeat sale model to estimate Quigley's (1995) hybrid model that is described above. Quigley's (1995) hybrid approach is a four-step procedure, where equation (7') is estimated separately using single and repeat sales, the residuals are used to estimate the parameters of (6"), and GLS weights are calculated from this and applied to (7') using the full sample of single and repeat sales. Recall that the hybrid model explicitly controls for changes in quality, as it makes use of both single sales and repeat sales. The vector of explanatory variables that captures franchise quality includes facility age, total championships that a team has won, the population of the market that the team plays in, and the franchise average winning percentage over the past 10 years, and a time dummy variable, [d.sub.it] measured in years from 1970 to 2009. Table 3 contains the results of steps 1, 2, and 4, which shows parameter estimates and p-values. The results from step 3, estimates of the unknown parameters in equation (6"), are available on request.

The estimated variance and standard errors calculations are described in the hybrid model section above. Column 1 contains the results for single sales, column 2 for only multiple sales, and column 3 the pooled regression with both single and multiple sales. From this regression, we can find the estimated variance [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and can calculate the estimated variance [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] based on the formula provided by Quigley (1995). Note that the regression with only multiple sales includes a franchise-dummy variable and indicator variables for new teams, teams in new locations, and teams that own their facility, which represents the individual-specific factors of franchises.

Also recall that the estimates of the parameters A and B in (6") identify and control for heteroscedasticity. Based on the estimates of A and B, the variance increases linearly with time elapsed since the previous sale, as the estimate of A is significant and positive and the estimate of B is not statistically significant. From these results, the GLS weights are derived and used to generate the results in column 3 on Table 3.

From both single sales and the pooled model, only population has a significant and positive parameter estimate. Franchises in larger markets are more valuable, other things equal. The parameter on the average winning percentage over the last 10 years is positive and significant in the single sale model only. Similar results were obtained from a model that used the average winning percentage over the last five years. Winning programs do not affect franchise values much, supporting the idea that professional sports teams in North America are profit maximizers, not win maximizers.

Again, the key summary statistic for the hybrid model is a quality-adjusted franchise price index that can be calculated from the year dummy variables in equation (7'). Figure 2 shows this price index. Note that the lags needed to estimate the error structure of the hybrid model means that we can only estimate the price index beginning in 1970.

[FIGURE 2 OMITTED]

Figure 2 tells a different story than Figure 1. Figure 2 shows a substantial increase in quality-adjusted franchise values beginning in the early 1990s. Figure 1 shows a peak in quality adjusted franchise values in the late 1980s or early 1990s and a decline thereafter.

Discussion

According to the repeat sales model, there was no substantial appreciation in franchise values over time. According to the hybrid model, which uses both single and repeat sales, franchise values of professional sports teams steadily increased over time beginning in the early 1990s. The results from a hedonic model in Humphreys and Mondello (2008), which uses single sales and does not account for repeat sales shows that the value of professional sports franchises increased steadily over time beginning in around 1980, a full 10 years earlier than the hybrid model results. The differences can be attributed to the underlying assumptions about franchise quality made by each model and the inclusion of variables controlling for observable franchise characteristics in the hybrid and hedonic models. The repeat sales model assumes that unobservable franchise quality is constant, and can be removed by only analyzing repeat sales. So, although the population or the facility age increases, the model does not account for the changes. The arguing point could be the population. From the results of the hybrid model, only population significantly and positively affects franchise values. In most markets, the population tends to increase over time, except for a few "rust belt" cities in the North and Northeast. Humphreys and Mondello (2008) found that population and franchise age increased franchise value in their hedonic model. The repeat sale quality-adjusted franchise price index indicates a different pattern in franchise price appreciation than the unconditional analysis by Fort (2006), the hybrid model, and the hedonic analysis by Humphreys and Mondello (2008).

The literature identifies four possible reasons for observed difference between quality adjusted price indexes based on the hedonic, hybrid, and repeat sales approaches:

1. Some important characteristics of each franchise change between transactions, while the repeat sales approach assumes that these characteristics remain unchanged, leading to bias in indexes derived from the repeat sales approach. In this context, the most important characteristics that change are the population of the market, the age of the franchise, and the age of the facility that the franchise plays in. Both increase over time, and the repeat sales approach does not account for this. Quigley's (1995) hybrid repeat sales method accounts for the effects of changes in market population and age-related factors in repeat sales methods. The results from this approach indicate that quality adjusted franchise prices began increasing rapidly in the early 1990s.

2. The prices of hedonic attributes change over time, while the repeat sales approach holds them constant, leading to bias in indexes derived from the repeat sales approach. Previous research suggests that local market population and income, private ownership of the facility, and on-field success are the most important observable hedonic characteristics in the market for professional sports franchises in North America. While we cannot rule out the possibility that the hedonic price of these characteristics has changed over time, it seems unlikely that underlying factors that affect the hedonic price of on-field franchise success in professional sports leagues should have changed over time, given the zero sum nature of wins in sports leagues. Similar reasoning applies to the hedonic price of a privately owned facility, given the instability of real estate markets.

3. The franchises that are bought and sold in the sample are not representative of the entire population of franchises, leading to selectivity bias in indexes derived from the repeat sales approach. No formal test exists to determine if the repeat sales analyzed here are representative of the overall sample of franchise sales in North America. But the repeat sales reported in Table 2 constitute 63% of the total sales reported in Table 1 for MLB, 51% of the total sales in the NBA, 45% of the sales in the NFL, and 40% of the sales in the NHL. Selectivity seems to be an unlikely culprit, given the relatively large number of franchises in the repeat sales sample.

4. The hedonic and hybrid approaches mis-specify the functional form of the model, and omit important hedonic characteristics from the model, leading to bias in indexes derived from the hedonic approach. The hedonic models used in the literature have been basic linear or linear-quadratic functions; no papers have used flexible functional forms. This makes the assessment of specification problems difficult, but leave ample room for mis-specification to be an important problem with indexes derived from hedonic models. There may be a number of franchise characteristics omitted from the hedonic model and hybrid, including tax benefits associated with owning professional sports teams, the fact that owning a sports team may be more valuable to some agents, like media corporations, than to others, and changes in the characteristics of modern sports facilities that began occurring after the opening of Camden Yards in Baltimore in 1992. The advent of the modern, entertainment-complex/sports facility began in the early 1990s, which coincides with the increase in the hybrid quality adjusted price index.

Of these four possible problems, bias due to mis-specification and omitted variables in hedonic models appears to contribute more to the observed difference between the quality adjusted franchise price index reported by Humphreys and Mondello (2008), the hybrid model, and the repeat sales model based indexes reported here. If correct, the implication is clear: the increase in the value of professional sports teams over the past 30 years cannot be attributed to general price increases in this market. The quality adjusted repeat sales index developed here has no upward trend; it appears to have peaked sometime in the late 1980s or early 1990s. The hybrid index increased in 1990. The increase in the value of sports franchises appears to be driven by characteristics of the franchises themselves, not to market appreciation.

Conclusions

Based on a repeat sales approach and a hybrid model incorporating both single and repeat sales, one quality adjusted North American professional sport franchise index developed here has no upward trend over the past 40 years, while the other increases markedly after 1990. The repeat sale quality adjusted price index appears to have peaked decades ago, indicating that the large increases in franchise prices documented by Fort (2006) cannot be attributed to market wide forces. Put another way, changes in the quality of individual franchises appear to drive increases in the value of professional sports franchises. Based on the results from hedonic and hybrid models of franchise values, the main factors associated with franchise quality are market income and population, facility characteristics, and on-field success. Market income and population have both increased significantly over the past century in North America. The four major professional sports leagues operate as monopolies in North America, and therefore restrict the number of franchises in order to generate monopoly rents. This restriction in the number of franchises in the face of increasing population and income clearly drives some of the increase in franchise values reported by Fort (2006).

Facility characteristics also affect franchise quality. Zimbalist and Long (2006) document an explosion in new facility construction in professional sports beginning in the early 1990s, and also show that public funds constituted an increasing fraction of money used to finance this stadium and arena construction boom. The hedonic based quality adjusted franchise price index in Humphreys and Mondello (2008) increases sharply after the mid-1980s, suggesting that general market conditions in the market for professional sports franchises contributed to much of the recent increases in professional sports franchises. This result also suggested that the increasing subsidies for new facility construction (as well as the increasing monopoly rents discussed in the previous paragraph) were not the only factors driving recent franchise price increases. Our results paint a less rosy picture. Since the repeat sales based quality adjusted price index declines over time, factors like the increasing subsidies for new sports facility construction appear to contribute much more to increases in professional sports franchise values than was previously thought. While these new facilities enhance the experience of fans attending games by providing improved sight lines, seats, and amenities, the also appear to line the pockets of wealthy sports team owners by ensuring that they will realize large capital gains when selling the franchise.

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Authors' Note

The authors would like to thank Gary Deeds for valuable research assistance.

Brad R. Humphreys and Yang Seung Lee

University of Alberta

Brad R. Humphreys is a professor in the Department of Economics and chair in the economics of gaming. His current research focuses on the economic impact of professional sports and the economics of sports gambling.

Yang Seung Lee is a post-doctoral fellow in the Department of Economics. His research focuses on applied microeconomic theory and its estimation.

Table 1: Franchise Sales Prices 1960-2009

Sport # Sales Mean St. Dev. Min Max
 Nominal Price

MLB 80 124.37 168.99 4.5 889.5
NBA 77 159.93 322.67 2.0 2125.0
NFL 56 212.29 296.83 1.4 1222.2
NHL 62 85.39 97.83 2.0 575.0

Table 2: Repeat Sales 1967-2009

Sport # Repeat Sales % Change St. Dev. Min Max

MLB 50 115% 1.21 -68% 409%
NBA 39 122% 1.04 -41% 377%
NFL 25 104% 0.87 -40% 343%
NHL 25 119% 1.16 61% 331%

Table 3: Regression Results, Hybrid Model

Variable Single Sales Repeat Sales All Sales

Facility Age 0.0007 0.008 -0.002
 (0.789) (0.173) (0.589)
Winning % Last 10 Years 0.746 0.855 0.522
 (0.001) (0.151) (0.114)
Championships Won -0.011 -0.001 -0.026
 (0.380) (0.953) (0.163)
Market Population 0.004 0.003 0.006
 (0.001) (0.533) (0.001)
Constant 2.048 -0.932 1.962
 (0.001) (0.395) (0.001)
Franchise Dummy? No Yes No
[??]
[??] 0.362 0.432
[??] - 0.005 -
R2 - 0.948 -
 0.87 0.51 0.78

p-values in parentheses.