- Email: [email protected]
Econometric analysis of copyrights
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Journal of Econometrics 139 (2007) 303–317 www.elsevier.com/locate/jeconom
Econometric analysis of copyrights Daniel J. Slottjea,b,, Daniel L. Millimetb, Michael J. Buchanana a FTI Consulting, Inc., USA Department of Economics, Southern Methodist University, P.O. Box 0496, Dallas, TX, USA
b
Available online 29 November 2006
Abstract This paper explores the impact of copyrights on firm value and on the demand for firm output. Using panel data on franchise value and ticket sales from the National Football League over the 1991–2000 period, we analyze the effect of copyrights (in this case, team logos) using several parametric estimators, the Arellano and Bond [1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297] dynamic panel data estimator, and a semi-non-parametric method based on difference-indifferences propensity score matching. We find a negative effect of logo changes on franchise value that is robust across multiple specifications. In addition, logo changes also appear to have a moderate positive, albeit not particularly robust, impact on ticket sales. r 2006 Elsevier B.V. All rights reserved. JEL classification: C14; C23; L83; M31 Keywords: Copyright; Dynamic panel data; Propensity score matching
1. Introduction Perhaps the single most important change in many businesses today is the understanding that intellectual property is a valuable (and in many cases undervalued) asset that many firms possess. In this paper, we explore the impact (if any) of one form of intellectual
Corresponding author. Department of Economics, Southern Methodist University, P.O. Box 0496, Dallas, TX, USA. Tel.: +1 75275 0496; fax: +1 214 768 1821. E-mail address: [email protected] (D.J. Slottje).
0304-4076/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jeconom.2006.10.013
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property, copyrights, on firm value and on the demand for firm output. Title 17 of the United States Code Section 102 defines a copyright as yoriginal works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced or otherwise communicated, either directly or with the aid of a machine or deviceyThis includes pictorial, graphic and sculptural works. The form of copyright that we focus on in this analysis is logos of professional sports teams. Our interest in this topic began when one of the authors was retained as a damages expert in a litigation matter involving logo infringement for a franchise in the National Football League (NFL). The matter is an intellectually interesting one because Title 17 of the United States Code Section 504(b) forms the basis for damages awarded by the Court for the infringement of a copyright and states: The copyright owner is entitled to recover y any profits of the infringer that are attributable to the infringement and are not taken into account in computing actual damages. In establishing the infringer’s profits, the copyright owner is required to present proof only of the infringer’s gross revenue, and the infringer is required to prove his or her deductible expenses and the elements of profit attributable to factors other than the copyrighted work. One may also look at this problem from the converse perspective of course, and ask the question: What is the marginal contribution of a copyright to a firm’s profits, ceteris paribus? To examine that question in the litigation matter, we constructed an econometric model, although other reasonable modes of analysis certainly may exist. Here, we are interested in a different issue, but this current body of research grew out of our work in the litigation matter. It is clear that firms value copyrights, are willing to spend great sums of money to protect copyrights, and that firms are willing to expend significant resources to litigate over copyright infringement. If firms are cognizant of the potential value of their copyrights, a meaningful exercise is to see if their copyrights are correlated with firm value and further, to see if copyrights can impact the demand for the products that firms produce. The previous empirical literature in this area is extremely limited. There are a few papers, for example, see Schankerman and Pakes (1986), Pakes (1985, 1986), and Lanjouw et al. (1998), that attempt to value patent rights held by firms in Europe using data on patents, patent renewals, and stock returns. However, to our knowledge, this is the first empirical study to attempt to quantify the value of copyrights. In this paper, we analyze the impact of copyrights on the value of NFL franchises and on the demand for watching NFL contests as measured by team attendance. NFL franchises possess a number of assets, any of which may be affected by copyrights. Most obvious is merchandising rights, but players, various concessions from the franchises’ home cities (e.g., tax funds to defray stadium costs), luxury box sales, etc. constitute other valuable ‘‘assets’’ owned by NFL teams. Since franchise value represents a summary measure of many of these factors, is publicly available (discussed further in Section 2.1), and is the analogue to firm value in professional sports, we utilize it as one outcome of interest. Team attendance represents an observable component of demand for firm output,
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may signal future changes in firm value ceteris paribus, and is also publicly available. We therefore utilize it as a second measure. The copyright impact is empirically identified because of variation in the data that arises from teams periodically altering their logos. By changing logos, these teams provide a measurable event that can be assessed to see if new copyrights impact franchise value and consumer demand. A priori one would expect logo changes to positively affect franchise value and ticket sales since the production of new logos is costly and, in the absence of any positive effects, there is no reason to incur such costs. To estimate the impact of a logo change on subsequent franchise valuation and ticket sales, we utilize panel data from 1991 to 2000, along with several econometric techniques. First, we utilize several straightforward parametric panel models, controlling for timeinvariant unobservable attributes of franchises that may be correlated with the decision to undertake logo changes as well as franchise value and consumer demand. Second, because more valuable franchises and franchises facing greater consumer demand tend to reinvent their logo more often, we estimate Arellano–Bond’s (1991) dynamic panel specification, explicitly controlling for lagged values of the outcomes of interest as well as time invariant, franchise-specific attributes. Finally, we utilize a difference-in-differences (DID) semi-nonparametric propensity score matching method. While matching methods are applicable primarily to problems of selection on observables, panel data allows us to employ a DID matching estimator, similar to that in Heckman et al. (1997), Smith and Todd (2005), and List et al. (2003), to control for the presence of unobservables that under normal circumstances may lead to biased estimates. The results are intriguing. In terms of franchise value, while pooled OLS estimates suggest no copyright impact, feasible GLS models allowing the errors be groupwise heteroskedastic and follow an AR(1) process and the dynamic GMM estimator indicate a robust, negative, and statistically significant copyright effect. Specifically, a logo change reduces franchise value by 5–6%. Finally, while the DID matching estimator yields a similar point estimate (5%), the effect is not statistically significant given the small number of matched pairs. In terms of the copyright effect on consumer demand as measured by tickets sales, the majority of specifications and estimation techniques fail to uncover a statistically significant effect, although the point estimates are consistently positive, in the 5–7% range. The remainder of the paper is organized as follows. Section 2 discusses the data and outlines the empirical methodology. Section 3 presents the results. Section 4 concludes. 2. Data and methodology 2.1. Data The data set includes information on the 31 current NFL franchises and spans the period 1991–2000.1 The value of each franchise in each year is obtained from Forbes Magazine; annual attendance and other franchise attributes are public information. As stated previously, in principal the value of other franchise assets could have been examined as well. For instance, merchandise sales are presumably most directly affected by logo 1
Data limitations prevent us from utilizing data prior to 1991. Moreover, the Houston Texans did not begin play until the 2002–2003 season; thus, only 31 franchises.
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changes (if there is any impact) in professional sports. However, because the NFL mandates revenue-sharing among the franchises for revenue obtained from merchandise sales, television contracts, etc., franchise-specific data on such sources of revenue are not publicly available. Nonetheless, since franchise value reflects all of these underlying revenue streams, as well as accounts for the NFL’s revenue-sharing procedures, if there is a copyright effect, we still expect variation in franchise value to be systematically related to logo changes. Publicly available franchise-specific attributes available as controls are: whether or not the team has changed its logo from the preceding season, annual wins and losses, whether the team won or lost the Super Bowl in a given year, whether the franchise is new or relocated to a new city since the preceding season, the age of the franchise, the conference and division in which the team plays, and stadium capacity. Finally, we also utilize controls for the socio-economic characteristics of each franchise’s home market: population, per capita income, and the local unemployment rate (obtained from the US Bureau of Economic Analysis). Summary statistics, disaggregated by logo changers and non-changers, are provided in Table 1. Over the 10-year period analyzed, we observe 14 logo changes. While additional Table 1 Summary statistics, 1991–2000 Variable
Logo Changers
Franchise value (millions US$) Tickets sold (100,000 s) Franchise age (years) New team (1 ¼ Yes) Relocated team (1 ¼ Yes) Wins (per season) Losses (per season) Super bowl champ (1 ¼ Yes) Super bowl loser (1 ¼ Yes) Stadium capacity (10,000 s) Population (millions) Per capita income (10,000 s US$) Unemployment rate
Non-changers
Mean
Std. dev.
Mean
Std. dev.
273.42
112.75
218.18
117.04
5.28
0.65
4.84
1.24
43.14
15.45
40.38
21.70
0.00
0.00
0.02
0.14
0.00
0.00
0.01
0.08
9.93
2.84
7.90
2.95
6.07
2.84
8.09
2.95
0.07
0.27
0.03
0.17
0.21
0.43
0.02
0.15
6.97
0.66
6.62
1.51
6.44
6.32
4.72
4.81
3.09
0.49
2.67
0.49
4.26
1.67
5.06
1.88
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variation would aid in identifying the copyright effect, as evidenced in the next section, we do not feel the relatively small number of logo changes inhibits one from obtaining a good understanding of the role of copyrights in accounting for the variation in franchise value and ticket sales. In terms of observable differences among franchises that altered their logos and those that did not, several interesting observations arise from Table 1. First, franchises that reinvented their logos were valued at roughly $55 million more than those that did not. However, franchises that reinvented their logo were valued at approximately $57 million more on average than franchises that did not undertake any logo changes the year prior to reinventing their logo. Thus, franchises that are more valuable to begin with are more likely to undertake logo changes. Second, consumer demand measured by ticket sales for franchises with new logos exceeded demand for those that retained previous logos by 44,000 on average; the average difference between soon-to-be logo changers and nonchangers in the year prior to the change was only 21,000. Third, the franchises with new logos were more successful—measured in terms of victories—than those that did not reinvent their logos, winning an average of two additional games per year; in the year prior to the change, the average difference in win total between soon-to-be logo changers and non-changers was 0.3. 2.2. Parametric approach To assess the impact of copyrights on franchise value and ticket sales in a statistical framework, we begin with several standard parametric panel data models. The parametric specifications used to estimate the effect of a logo change on franchise attributes are nested in the following estimating equation: lnðyit Þ ¼ ai þ lt þ dLit þ X it b þ it ,
(1)
where yit is the outcome of interest for franchise i in year t (i.e., franchise value or ticket sales); ai are franchise fixed effects; lt are year fixed effects; Lit is a binary variable taking a value of unity if a franchise changed its logo from the previous year, zero otherwise; Xit is a vector of franchise attributes to be controlled. The variables in X include: previous won/ loss record, controls for whether or not the team won the league championship or made it into the league championship game that year, dummy variables for whether the team is a new franchise or relocated from a different city, the seating capacity of the team’s home arena, and finally socio-economic characteristics of the franchises home metropolitan area (population, mean per capita income, and unemployment rate in that city). The most parsimonious specification we estimate restricts ai ¼ a for all i. This amounts to a simple pooled OLS regression, although we report standard errors that are robust to heteroskedasticity and arbitrary correlation of the residuals within franchises. Next, we relax the assumption that ai ¼ a, and include both franchise and year effects in (1). Again, we report robust standard errors. Third, we again impose the assumption of no franchisespecific heterogeneity, but we explicitly allow the error term to follow an AR(1) process, and for the variance of the residual to be franchise-specific. This is estimated by Feasible Generalized Least Squares (FGLS). Finally, we re-estimate the FGLS model allowing for both franchise- and year-specific effects. Before proceeding, three comments are in order. First, FGLS is more efficient than simply using pooled OLS with robust standard errors if the error structure is well specified.
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If it is not, the pooled OLS with robust standard errors is preferred. Tests of groupwise heteroskedasticity are conducted (Greene, 2000, p. 598). Second, our focus on the potential autoregressive nature of the error terms arises from the fact that unobservables such as fan support are likely to persist over short time periods. Finally, as the final two methods do not rely on the assumption of normality, we also conduct tests for normality of the residuals (Doornik and Hansen, 1994). 2.3. Dynamic panel approach An alternative specification is the dynamic panel model of Arellano and Bond (1991) estimated via the General Method of Moments (GMM). The benefit of this specification is that it explicitly conditions on lagged values of the dependent variable, while also controlling for unobserved franchise-specific heterogeneity. Thus, as opposed to allowing for autocorrelation in unobservable shocks to franchise value and/or ticket sales (e.g., trends in the popularity of the franchise), the model explicitly allows past levels of the outcome of interest to affect current levels. Moreover, as stated in Section 2.1, the decision to reinvent a franchise’s logo is positively correlated with ticket sales and franchise value. The model uses first-differences to remove time-invariant, franchise-specific attributes, and then uses twice-lagged (and higher orders) of the dependent variables as instruments for the lagged values of the dependent variable. Specifically, the model is given by S~ it ¼ ai þ lt þ yS~ it1 þ dLit þ X it b þ it , where S~ is the logarithm of franchise value or ticket sales. First-differencing yields
(2)
DS~ it ¼ Dlt þ yDS~ it1 þ DdLit þ DX it b þ Dit . (3) ~ Assuming the errors, eit, are not autocorrelated, DS it1 will still be correlated with the error term, Dit1 , in (3). However, S~ it2 , S~ it3 , etc. are available as instruments. If, on the other hand, eit is autocorrelated (or, equivalently, Deit follows an AR(2) process or higher), then the instruments will be invalid. Tests of autocorrelation and a Sargan test of the overidentifying restrictions are conducted, as in Arellano and Bond (1991). 2.4. Propensity score matching method An alternative method of assessing the impact of a discrete treatment on an outcome of interest is the method of propensity score matching developed in Rosenbaum and Rubin (1983). While extensively used by statisticians, economic applications have been sparse until recently. A few notable examples include Dehejia and Wahba (1999, 2002), Heckman et al. (1997, 1998), List et al. (2003), and Smith and Todd (2005). Blundell and Costa-Dias (2002) provide an excellent introduction to the matching method, concluding, ‘‘matching methods have been extensively refined in the recent evaluation literature and are now a valuable part of the evaluation toolbox’’ (p. 4). The fundamental problem in identifying treatment effects is one of incomplete information. While the econometrician observes whether the treatment occurs and the outcome conditional on treatment assignment, the counterfactual is unobserved. Let yi1 denote the outcome of observation i if the treatment occurs (given by Ti ¼ 1); yi0 denotes the outcome in the absence of treatment (Ti ¼ 0). If both states of the world were observable, the average treatment effect, t, would equal y1 y0 , where the former (latter)
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average represents the mean outcome for the treatment (control) group. However, given that only y1 or y0 is observed for each observation, unless assignment into the treatment group is random, generally tay1 y0 . The solution Rosenbaum and Rubin (1983) advocate is to find a vector of covariates, Z, such that y1 ; y0 ? TjZ;
prðT ¼ 1jZÞ 2 ð0; 1Þ,
(4)
where ? denotes independence. If one is interested in estimating the average treatment effect, only the weaker condition (40 ) E y0 jT ¼ 1; Z ¼ E y0 jT ¼ 0; Z ¼ E y0 jZ ; prðT ¼ 1jZÞ 2 ð0; 1Þ is required. To implement the matching technique, the treatment group is defined as the set of franchises that changed their logo from the preceding year. The outcome of interest, y, is the (logarithm of) franchise value or ticket sales. For condition (40 ) to hold, the conditioning set Z should be multi-dimensional. Consequently, finding observations with identical values for all covariates in Z may be untenable. However, Rosenbaum and Rubin (1983) prove that conditioning on p(Z) is equivalent to conditioning on Z, where pðZÞ ¼ prðT ¼ 1jZ Þ is the propensity score. p(Z) is estimated via a standard probit model. Upon estimation of the propensity score, a matching algorithm must be defined in order to estimate the missing counterfactual, y0i, for each treated observation i. The simplest algorithm is nearest-neighbor matching, whereby each treated observation is paired with the control observation whose propensity score is closest in absolute value (Dehejia and Wahba, 2002).2 Unmatched controls are discarded and the average treatment effect on the treated (TT) is (5) tTT ¼ E y1 T ¼ 1; pðZÞ E y0 T ¼ 0; pðZÞ ¼ E y1 y0 pðZÞ . The estimator in (5) will provide an unbiased estimate of TT only if condition (40 ) is satisfied. As such, matching is useful as a solution to problems of selection on observables. However, we amend the basic matching algorithm in two important ways to utilize our panel data and remove certain unobservables that may not be controlled by simply conditioning on the propensity score. First, we restrict the pool of potential controls to which a given treated observation may be paired. Specifically, we perform the matching exercise twice: (i) unrestricted matching, and (ii) restricting matched pairs to be from the same year. By matching within-year, we explicitly remove any time-specific unobservables not already controlled for by the propensity score. This is the matching method’s analogy to fixed effects, and is similar to the claims made in Smith and Todd (2005) that matches— used to identify the effect of employment programs—should be from the same labor market. Thus, the estimator in (5) becomes tTT;t ¼ E y1 T ¼ 1; pðZÞ; t E y0 T ¼ 0; pðZÞ; t ¼ E y1 y0 pðZÞ; t , (6) where t indexes year. 2 Typically nearest-neighbor matching is performed with replacement, implying that a given control observation may be matched to multiple treatment observations. Dehejia and Wahba (2002) verify that matching with replacement fares at least as well as matching without replacement and possibly better.
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Second, we employ a difference-in-differences (DID) matching estimator, similar to that used in Eichler and Lechner (2002), Heckman et al. (1997), and List et al. (2003). The strategy entails making an assumption of bias stability (BS) and requires data on both the treated and the controls prior to the treatment date. The idea is that although the condition in (40 ) may not hold due to the presence of unobservables, the bias detected prior to the actual treatment date may provide a reasonable estimate of the post-treatment bias. To see this, consider the method of matching more closely. The average treatment effect on the treated group in (5) is equivalent to tTT ¼ E E y1 T ¼ 1; pðZÞ E y0 T ¼ 1; pðZÞ ¼ E E y1 T ¼ 1; pðZÞ E y0 T ¼ 0; pðZÞ ,
(7) where the outer expectation is over the distribution of Z|T ¼ 1. If the conditional independence assumption in (40 ) does not hold, the bias, B, is given by (8) B ¼ E y0 T ¼ 1; pðZÞ E E y0 T ¼ 0; pðZÞ , where again the outer expectation of the second right-hand side term is over the distribution of Z|T ¼ 1. The bias, B, is estimated by the mean difference in franchise value or ticket sales prior to the treatment and is subtracted from the estimated treatment effect obtained in (5) or (6). For notation, we define the DID counterpart to (5) and (6) as tDID ¼ tTIT t0TT ,
(9a)
tDID;t ¼ tTIT;t t0TT;t ,
(9b)
where t0 TT, t0 TT,t are the mean differences in lagged franchise value or ticket sales across the matched treatment and control groups in the unrestricted and restricted cases, respectively. Upon completing the matching estimation, balancing tests are conducted. Balancing refers to the fact that after conditioning on the propensity score and obtaining the matched sub-sample, the distribution of the conditioning variables, Z, should not differ across the treatment and control group. Thus, after matching, we also test for differences in the mean of the Z’s. Finally, prior to continuing, it is important to highlight the differences between matching estimators and the estimators from the previous section. First, the matching estimator entails relatively few distributional assumptions. Second, matching allows for non-parametric interactions between all the covariates in Z in the determination of the outcome of interest (Bratberg et al. 2002). Finally, matching estimators identify a restricted sub-sample of control observations that are most ‘‘similar’’ to the treatment group, whereas the previous models utilize all available observations. While this may be a positive to the extent that control observations deemed too different from the treatment group are excluded, in applications with few treated observations this leads to small sample sizes. 3. Empirical results 3.1. Parametric estimates Table 2 presents the estimates from the four specifications discussed in Section 2.2. The coefficient estimates of primary interest are displayed in bold. In the interest of brevity, we
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only report the coefficient on logo change (the full set of results are available upon request). Columns 1–4 display the results for franchise value; columns 5–8 present the results for ticket sales. In terms of the copyright impact on franchise value, the simple pooled OLS model with time effects and a no franchise-specific heterogeneity (column 1) indicates that logo changes have a negative, albeit statistically insignificant, impact on franchise value (d^ ¼ 0:02, robust standard error ¼ 0.04). Allowing the intercept to vary by franchise (column 2) yields a similar same result (d^ ¼ 0:03, robust standard error ¼ 0.03), despite the fact that we reject the null of equal intercepts across franchises (F ¼ 7.85, P ¼ 0.00). Columns 3 and 4 present the FGLS results with (column 4) and without (column 3) franchise-specific intercepts. The FGLS models allow for groupwise heteroskedasticity and AR(1) errors. As this imposes a specific structure on the errors, the results are more efficient than the pooled OLS results with robust standard errors if the error structure is correctly specified. As in the pooled OLS models, while we easily reject the null of no franchise-specific heterogeneity (w2 ¼ 158.72, P ¼ 0.00), the copyright effect is virtually ^ ^ unaffected, with the point estimates being d ¼ 0:06 d ¼ 0:05 in column 3 (4). Furthermore, both estimates are statistically significant at the 95% confidence level. The fact that the point estimates of the copyright effect on franchise value are negative, with some even statistically significant, is surprising since, as stated previously, undertaking logo changes is costly and there does not appear to be any motivation to do so unless there is an economic benefit. Thus, we turn to some diagnostic tests of these specifications. First, tests for groupwise heteroskedasticity in the pooled OLS model with franchise-specific effects and both FGLS models clearly reject the null of a constant residual variance across franchises, thus validating our use of robust standard errors or explicit allowance for the variance to vary across franchises. Second, in all four models, the test for normality of the residuals overwhelmingly rejects the null in every case. While this may invalidate hypothesis tests, it does not affect the negative point estimates. Consequently, we examine the robustness of these findings through the use of alternative estimation methods. Prior to examining these additional results, columns 5–8 in Table 2 display the analogous pooled OLS and FGLS results for the impact of copyrights on ticket sales. In all four specifications, the copyright impact is statistically insignificant and the point estimates are extremely close to zero. Thus, we fail to find any influence of logo changes on the demand for NFL franchise output as measured by in-person viewing of games. In terms of the diagnostic tests, the results are similar to those in the models examining for franchise value. Specifically, we find significant evidence of franchise-specific heterogeneity (although such heterogeneity does not affect the estimated copyright effect), groupwise heteroskedasticity, and we consistently reject the null of normality. 3.2. Dynamic panel estimates The results using the Arellano and Bond (1991) GMM estimator are presented in Tables 3 (franchise value) and 4 (ticket sales). For each outcome, four specifications are estimated: (i) conditioning on (one-period) lagged values of the dependent variable; (ii) conditioning on (one-period) lagged values of the dependent variables and measures of franchise success (i.e., wins and Super Bowl victories and defeats); (iii) conditioning on
312
Table 2 Parametric estimates of the logo effect Franchise value
Ticket sale
Pooled OLS
Pooled OLS
GLS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.02 (0.04) No
0.03 (0.03) Yes
0.06* (0.02) No
0.05* (0.02) Yes
0.01 (0.03) No
0.01 (0.02) Yes
0.00 (0.01) No
2.3 1003 (0.01) Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
w2(9) ¼ 693.80 (P ¼ 0.00) w2(28) ¼ 158.72 (P ¼ 0.00)
F(9, 274) ¼ 1.05 (P ¼ 0.43)
F(9, 274) ¼ 2.02 (P ¼ 0.07) F(30, 244) ¼ 11.22 (P ¼ 0.00) w2(31) ¼ 7.4*1026 (P ¼ 0.00)
w2(9) ¼ 6.53 (P ¼ 0.69)
w2(9) ¼ 8.14 (P ¼ 0.52) w2(29) ¼ 327.10 (P ¼ 0.00)
w2(31) ¼ 5.9*1006 (P ¼ 0.00)
w2(30) ¼ 2.2*1024 (P ¼ 0.00)
w2(2) ¼ 110.09 (P ¼ 0.00) 294
w2(2) ¼ 364.40 (P ¼ 0.00) 294
w2(2) ¼ 118.24 (P ¼ 0.00) 294
F(9, 270) ¼ 48.15 F(8, 241) ¼ 43.69 w2(9) ¼ 780.82 (P ¼ 0.00) (P ¼ 0.00) (P ¼ 0.00) F(30, 241) ¼ 7.85 (P ¼ 0.00)
w2(2) ¼ 53.16 (P ¼ 0.00) 291
w2(31) ¼ 3220.75 (P ¼ 0.00)
w2(30) ¼ 1270.46 (P ¼ 0.00)
w2(30) ¼ 1945.38 (P ¼ 0.00)
w2(2) ¼ 30.44 (P ¼ 0.00) 291
w2(2) ¼ 85.75 (P ¼ 0.00) 290
w2(2) ¼ 24.38 (P ¼ 0.00) 290
w2(2) ¼ 163.38 (P ¼ 0.00) 294
Notes: Each specification also includes controls for: franchise age, number of wins, whether the team won the league championship, whether the team lost in the league championship, arena capacity, total ticket sales, and the population, unemployment rate, and mean per capita income of the franchise’s home metropolitan area. GLS models allow for groupwise heteroskedasticity and AR(1) errors, with a common correlation coefficient. Standard errors or P-values in parentheses; standard errors in pooled OLS models are robust to arbitrary heteroskedasticity and correlation within franchises. Test for groupwise heteroskedasticity based on Greene (2000, p. 598). Omnibus test for normality based on Doornik and Hansen (1994). *Indicates significant at 5% level. **Indicates significant at 10% level.
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Logo change (1 ¼ Yes) Franchise Effects Year Effects Joint significance of year effects Joint significance of Franchise effects Modified Wald test for groupwise heteroskedasticity Omnibus test for normality Observations
GLS
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Independent variable
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one-period lagged values of the dependent variables and one- and two-period measures of franchise success; and, (iv) conditioning on one- and two-period lagged values of the dependent variables and measures of franchise success. All specifications also include controls for the contemporaneous values of the remaining franchise attributes. In addition to reporting the most relevant coefficient estimates, we also report the results of the Sargan overidentification test and the test for no autocorrelation (in the non-differenced data). All four specifications in Table 3 find a negative and statistically significant (at the 95% confidence level) effect of logo changes on franchise value. Specifically, as in the FGLS models in Table 2 that explicitly allowed for autocorrelation, a logo change is associated with an average decline in franchise value of 5–6%. Moreover, franchise value is found to be highly persistent over time as lagged values are positively related to current value, as one would expect. Finally, the Sargan test and test for no autocorrelation indicate that all models are well specified with regards to the validity of the instruments and the assumptions concerning the errors. In terms of ticket sales, Table 4 reports a consistent point estimate of 0.05–0.06 across the four specifications; however, only the estimate in column 1 is statistically significant at the 90% level. While the specifications in columns 2–4 find a similar logo effect as in Table 3 GMM estimates of the logo effect on franchise value Independent variable Logo change (1 ¼ Yes) Lagged ln(value) Twice-lagged ln(value) Lagged Success Variables Twice-lagged Success Variables Franchise Effects Year Effects Joint significance of year effects Sargan Over identification Test Ho: No autocorrelation
(1)
(2) *
(3) *
(4) *
0.05 (0.02) 0.26** (0.14) —
0.06 (0.02) 0.29* (0.14) —
0.06 (0.02) 0.35* (0.15) —
No
Yes
Yes
0.06* (0.02) 0.51* (0.16) 0.10 (0.07) Yes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
w2(7) ¼ 331.11 (P ¼ 0.00) w2(35) ¼ 9.60 (P ¼ 1.00)
w2(6) ¼ 253.36 (P ¼ 0.00) w2(35) ¼ 9.57 (P ¼ 1.00)
w2(6) ¼ 305.36 (P ¼ 0.00) w2(35) ¼ 7.90 (P ¼ 1.00)
w2(6) ¼ 246.03 (P ¼ 0.00) w2(33) ¼ 5.82 (P ¼ 1.00)
P ¼ 0.22
P ¼ 0.20
P ¼ 0.21
P ¼ 0.45
Notes: Each specification also includes controls for: number of wins, whether the team won the league championship, whether the team lost in the league championship, arena capacity, and the population, unemployment rate, and mean per capita income of the franchise’s home metropolitan area. ‘‘Success variables’’ include wins and dummy variables indicating that the team either won the league championship or lost in the league championship. Robust standard errors or P-values in parentheses. *Indicates significant at 5% level. **Indicates significant at 10% level.
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Table 4 GMM estimates of the logo effect on ticket sales Independent Variable Logo change (1 ¼ Yes) Lagged ln(ticket sales) Twice-lagged ln(ticket sales) Lagged Success Variables Twice-lagged Success Variables Franchise Effects Year Effects Joint significance of year effects Sargan Over identification Test Ho: No autocorrelation
(1)
(2)
(3)
(4)
0.06** (0.04) 0.52* (0.13) — (0.14) No
0.06 (0.04) 0.46* (0.14) —
0.06 (0.04) 0.43* (0.15) —
0.05 (0.04) 0.44* (0.15) 0.11
Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
w2(7) ¼ 11.65 (P ¼ 0.11) w2(35) ¼ 5.08 (P ¼ 1.00)
w2(6) ¼ 8.04 (P ¼ 0.24) w2(35) ¼ 6.11 (P ¼ 1.00)
w2(6) ¼ 8.21 (P ¼ 0.22) w2(35) ¼ 2.46 (P ¼ 1.00)
w2(6) ¼ 7.28 (P ¼ 0.30) w2(33) ¼ 3.75 (P ¼ 1.00)
P ¼ 0.90
P ¼ 0.93
P ¼ 0.98
P ¼ 0.53
Notes: See Table 3.
column 1, the standard errors increase sufficiently such that the logo effect is no longer statistically significant at conventional levels. Finally, as in Table 3, all four specifications fair well in terms of the Sargan test and test for no autocorrelation, as well as find a positive and statistically significant effect of lagged values of the dependent variable as one would expect if fan loyalty and season ticket sales change slowly over time. 3.3. Propensity score matching estimates The final estimation technique is the semi-non-parametric propensity score matching method. The results are shown in Table 5. Column 1 (2) shows the mean differences between the matched treatment (logo changers) and control group (logo non-changers) using the unrestricted (within-year) matching algorithm. The average difference in the propensity score across the matched pairs is 0.05 with unrestricted matching; 0.10 under within-year matching. Neither difference is statistically significant (unrestricted: P ¼ 0.54; within-year: P ¼ 0.22). In addition, prior to discussing the various estimates of the treatment effects, we note that the differences between the matched treatment and control group in terms of the various observed attributes are never statistically significant at the 95% confidence level. Moreover, we never reject the null of joint equality of the means of the various control variables using a Hotelling T2-tests (unrestricted matching: F ¼ 0.38, P ¼ 0.96; within-year matching: F ¼ 0.34, P ¼ 0.97).
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Table 5 Propensity score estimates of the logo effect Independent variable
Propensity score ln(value) (tTT,K) Lagged value D ln(value) (tDID,) ln(ticket sales) (tTT,) Lagged ticket Sales D ln(ticket sales) (tDID,) Wins Super bowl champion (1 ¼ Yes) Super bowl loser Population (millions) Unemployment Rate (0-100) Per capita Income (1000 s) Franchise age (years) Stadium Capacity (1000 s) AFC east (1 ¼ Yes) AFC central (1 ¼ Yes) AFC west (1 ¼ Yes) NFC east (1 ¼ Yes) NFC central (1 ¼ Yes) NFC West (1 ¼ Yes) Hotelling T2 Number of Matched pairs Number of Unique controls
Matching algorithm Unrestricted (1)
Within-year (2)
0.05 (P ¼ 0.54) 0.23 (P ¼ 0.19) 0.26 (P ¼ 0.11) 0.03 (P ¼ 0.52) 0.05 (P ¼ 0.37) 0.06 (P ¼ 0.43) 0.11 (P ¼ 0.06) 0.43 (P ¼ 0.66) 0.07 (P ¼ 0.33) 0.00 (P ¼ 1.00) 1.02 (P ¼ 0.67) 0.51 (P ¼ 0.52) 0.80 (P ¼ 0.72) 4.21 (P ¼ 0.40) 0.86 (P ¼ 0.80) (1) 0.36 (P ¼ 0.06) 0.14 (P ¼ 0.30) 0.00 (P ¼ 1.00) 0.07 (P ¼ 0.56) 0.00 (P ¼ 1.00) 0.14 (P ¼ 0.30) F(14, 13) ¼ 0.38 (P ¼ 0.96) 14
0.10 (P ¼ 0.22) 0.02 (P ¼ 0.91) 0.03 (P ¼ 0.86) 0.05 (P ¼ 0.19) 0.06 (P ¼ 0.29) 0.01 (P ¼ 0.94) 0.07 (P ¼ 0.22) 0.50 (P ¼ 0.63) 0.00 (P ¼ 1.00) 0.14 (P ¼ 0.30) 0.92 (P ¼ 0.67) 0.78 (P ¼ 0.15) 0.65 (P ¼ 0.74) 5.50 (P ¼ 0.38) 1.32 (P ¼ 0.61) (2) 0.07 (P ¼ 0.68) 0.07 (P ¼ 0.64) 0.07 (P ¼ 0.56) 0.07 (P ¼ 0.64) 0.00 (P ¼ 1.00) 0.00 (P ¼ 1.00) F(14, 13) ¼ 0.34 (P ¼ 0.97) 14
12
12
Notes: Parameter estimates refer to the mean difference between the matched treatment and control group, where observations in the control group are weighted by the number of times they appear. P-values are associated with the null that the means are equal across the treatment and control groups. ‘‘Unique controls’’ reports the number of controls that are matched with at least one treatment observation.
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In terms of the estimated copyright effect on franchise value, the franchise value of teams that reinvented their logos exceeds the value of those that did not by 23% on average using the unrestricted matching algorithm, although the difference is not statistically significant (P ¼ 0.19). However, as stated previously, if assignment to the treatment group is based on unobservables and these unobservables are associated with franchise value, then the matching estimate of the average treatment effect will be biased. Thus, we turn to the DID estimator. Here, we see that the lagged franchise value of logo changers exceeds that for logo non-changes by 26% (although this difference is not statistically significant; P ¼ 0.11). Consequently, the DID estimate of the average treatment effect is 3%. While not statistically significant given the availability of only 14 matched pairs (P ¼ 0.52), the point estimate differs very little from those reported in Tables 2 and 3 by the previous econometric methods. Although not discussed previously, in Tables 2 and 3 we always reject the null of no time effects. Given the importance of the time effects in explaining franchise value, the withinyear matching estimators are preferred. Examining the within-year matching results shows that while the average differences in current and lagged franchise value across logo changers and non-changers are vastly different than those obtained by the unrestricted matching (although both remain statistically insignificant), the preferred DID estimate is virtually unchanged, suggesting that logo changers suffer a change in franchise value of 5% (P ¼ 0.19). Thus, matching within-year and utilizing the DID approach yields an estimate that is nearly identical to those displayed in Tables 2 and 3, with the lack of statistical significance reflecting the fact that the matching estimates are based on a smaller sample size as unmatched controls are discarded. Nonetheless, the negative copyright effect on franchise value is robust across all methodologies and modeling assumptions. In terms of ticket sales, the unrestricted and within-year matching finds that logo changers have 5–6% greater ticket sales than logo non-changers on average. Moreover, lagged ticket sales for non-changers exceed that for changers by 1–6%. Thus, the DID estimates of the copyright effect on consumer demand as measured by ticket sales is 11% (7%) according to the unrestricted (within-year) matching, with the unrestricted matching estimate being statistically significant at the 90% confidence level despite the small sample size (P ¼ 0.06). Moreover, since the null of no time effects is not rejected at the 95% confidence level in all specifications in Tables 2 and 4, the unrestricted matching estimates are preferred as unrestricted matching allows matched pairs that have more similar propensity scores. Overall, then, the various methodologies suggest a less robust, but positive, copyright effect on consumer demand. 4. Concluding remarks This paper analyzed the impact of copyrights on firm values and on the demand for firm output. The copyright in question is logos of professional football teams in the United States. Using several parametric estimators, the Arellano and Bond (1991) dynamic panel estimator, and a semi-non-parametric method based on difference-in-differences propensity score matching, we find a negative and statistically significant impact on franchise value, robust across most methodologies, and at best a marginally significant positive impact on ticket sales. Given that the invention of new logos is costly and there does not appear to any benefit of undertaking a logo change that should not be incorporated into the value of the franchise (e.g., merchandise sales, fan appeal, appeal to players, etc.), the
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negative effect on franchise value is particularly startling. Moreover, if franchise value incorporates consumer demand, then not only is there a net negative effect of logo changes on franchise value, but logo changes must result in some negative effects that more than offset the (marginal) positive effect on ticket sales. As this is the first empirical study, to our knowledge, attempting to quantify the impact of copyrights on firms, clearly future research into the understanding what these negative effects are, and if other forms of copyrights yield similar negative impacts, is warranted. Acknowledgments The authors thank Michael McAleer, two anonymous referees, and participants at the Australasian Meeting of the Econometric Society, July 2002, for helpful comments and suggestions. References Arellano, M., Bond, S., 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297. Blundell, R., Costa-Dias, M., 2002. Alternative approaches to evaluation in empirical microeconomics. Portuguese Economic Journal 1, 91–115. Bratberg, E., Grasdal, A., Risa, A.E., 2002. Evaluating social policy by experimental and nonexperimental methods. Scandanavian Journal of Economics 104, 147–171. Dehejia, R.H., Wahba, S., 1999. Casual effects in nonexperimental studies: reevaluating the evaluation of training programs. Journal of the American Statistical Association 94, 1053–1062. Dehejia, R.H., Wahba, S., 2002. Propensity score matching for nonexperimental causal studies. Review of Economics and Statistics 84, 151–161. Doornik, J.A., Hansen, H., 1994. An omnibus test for univariate and multivariate normality. Unpublished manuscript, Nuffield College, Oxford University. Eichler, M., Lechner, M., 2002. An evaluation of public employment programmes in the East German state of sachsen-anhalt. Labour Economics 9, 143–186. Greene, W., 2000. Econometric Analysis. Prentice-Hall, Upper Saddle River, NJ. Heckman, J.J., Ichimura, H., Todd, P.E., 1997. Matching as an econometric evaluation estimator: evidence from evaluating a job training program. Review of Economic Studies 64, 605–654. Heckman, J.J., Ichimura, H., Todd, P.E., 1998. Matching as an econometric evaluation estimator. Review of Economic Studies 65, 261–294. Lanjouw, J.O., Pakes, A., Putnam, J., 1998. How to count patents and value intellectual property: uses of patent renewal and application data. Journal of Industrial Economics 46, 405–433. List, J.A., Millimet, D.L., Fredriksson, P.G., McHone, W.W., 2003. Effects of environmental regulations on manufacturing plant births: evidence from a propensity score matching estimator. Review of Economics and Statistics 85, 944–952. Pakes, A., 1985. On patents, R and D, and the stock market rate of return. Journal of Political Economy 93, 390–409. Pakes, A., 1986. Patents as options: some estimates of the value of holding European patent stocks. Econometrica 54, 755–784. Rosenbaum, P., Rubin, D., 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41–55. Schankerman, M., Pakes, A., 1986. Estimates of the value of patent rights in European countries during the post1950 period. The Economic Journal 96, 1052–1076. Smith, J., Todd, P.E., 2005. Does matching address lalonde’s critique of nonexperimental estimators. Journal of Econometrics 125, 305–353.
Journal of Econometrics 139 (2007) 303–317 www.elsevier.com/locate/jeconom
Econometric analysis of copyrights Daniel J. Slottjea,b,, Daniel L. Millimetb, Michael J. Buchanana a FTI Consulting, Inc., USA Department of Economics, Southern Methodist University, P.O. Box 0496, Dallas, TX, USA
b
Available online 29 November 2006
Abstract This paper explores the impact of copyrights on firm value and on the demand for firm output. Using panel data on franchise value and ticket sales from the National Football League over the 1991–2000 period, we analyze the effect of copyrights (in this case, team logos) using several parametric estimators, the Arellano and Bond [1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297] dynamic panel data estimator, and a semi-non-parametric method based on difference-indifferences propensity score matching. We find a negative effect of logo changes on franchise value that is robust across multiple specifications. In addition, logo changes also appear to have a moderate positive, albeit not particularly robust, impact on ticket sales. r 2006 Elsevier B.V. All rights reserved. JEL classification: C14; C23; L83; M31 Keywords: Copyright; Dynamic panel data; Propensity score matching
1. Introduction Perhaps the single most important change in many businesses today is the understanding that intellectual property is a valuable (and in many cases undervalued) asset that many firms possess. In this paper, we explore the impact (if any) of one form of intellectual
Corresponding author. Department of Economics, Southern Methodist University, P.O. Box 0496, Dallas, TX, USA. Tel.: +1 75275 0496; fax: +1 214 768 1821. E-mail address: [email protected] (D.J. Slottje).
0304-4076/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jeconom.2006.10.013
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property, copyrights, on firm value and on the demand for firm output. Title 17 of the United States Code Section 102 defines a copyright as yoriginal works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced or otherwise communicated, either directly or with the aid of a machine or deviceyThis includes pictorial, graphic and sculptural works. The form of copyright that we focus on in this analysis is logos of professional sports teams. Our interest in this topic began when one of the authors was retained as a damages expert in a litigation matter involving logo infringement for a franchise in the National Football League (NFL). The matter is an intellectually interesting one because Title 17 of the United States Code Section 504(b) forms the basis for damages awarded by the Court for the infringement of a copyright and states: The copyright owner is entitled to recover y any profits of the infringer that are attributable to the infringement and are not taken into account in computing actual damages. In establishing the infringer’s profits, the copyright owner is required to present proof only of the infringer’s gross revenue, and the infringer is required to prove his or her deductible expenses and the elements of profit attributable to factors other than the copyrighted work. One may also look at this problem from the converse perspective of course, and ask the question: What is the marginal contribution of a copyright to a firm’s profits, ceteris paribus? To examine that question in the litigation matter, we constructed an econometric model, although other reasonable modes of analysis certainly may exist. Here, we are interested in a different issue, but this current body of research grew out of our work in the litigation matter. It is clear that firms value copyrights, are willing to spend great sums of money to protect copyrights, and that firms are willing to expend significant resources to litigate over copyright infringement. If firms are cognizant of the potential value of their copyrights, a meaningful exercise is to see if their copyrights are correlated with firm value and further, to see if copyrights can impact the demand for the products that firms produce. The previous empirical literature in this area is extremely limited. There are a few papers, for example, see Schankerman and Pakes (1986), Pakes (1985, 1986), and Lanjouw et al. (1998), that attempt to value patent rights held by firms in Europe using data on patents, patent renewals, and stock returns. However, to our knowledge, this is the first empirical study to attempt to quantify the value of copyrights. In this paper, we analyze the impact of copyrights on the value of NFL franchises and on the demand for watching NFL contests as measured by team attendance. NFL franchises possess a number of assets, any of which may be affected by copyrights. Most obvious is merchandising rights, but players, various concessions from the franchises’ home cities (e.g., tax funds to defray stadium costs), luxury box sales, etc. constitute other valuable ‘‘assets’’ owned by NFL teams. Since franchise value represents a summary measure of many of these factors, is publicly available (discussed further in Section 2.1), and is the analogue to firm value in professional sports, we utilize it as one outcome of interest. Team attendance represents an observable component of demand for firm output,
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may signal future changes in firm value ceteris paribus, and is also publicly available. We therefore utilize it as a second measure. The copyright impact is empirically identified because of variation in the data that arises from teams periodically altering their logos. By changing logos, these teams provide a measurable event that can be assessed to see if new copyrights impact franchise value and consumer demand. A priori one would expect logo changes to positively affect franchise value and ticket sales since the production of new logos is costly and, in the absence of any positive effects, there is no reason to incur such costs. To estimate the impact of a logo change on subsequent franchise valuation and ticket sales, we utilize panel data from 1991 to 2000, along with several econometric techniques. First, we utilize several straightforward parametric panel models, controlling for timeinvariant unobservable attributes of franchises that may be correlated with the decision to undertake logo changes as well as franchise value and consumer demand. Second, because more valuable franchises and franchises facing greater consumer demand tend to reinvent their logo more often, we estimate Arellano–Bond’s (1991) dynamic panel specification, explicitly controlling for lagged values of the outcomes of interest as well as time invariant, franchise-specific attributes. Finally, we utilize a difference-in-differences (DID) semi-nonparametric propensity score matching method. While matching methods are applicable primarily to problems of selection on observables, panel data allows us to employ a DID matching estimator, similar to that in Heckman et al. (1997), Smith and Todd (2005), and List et al. (2003), to control for the presence of unobservables that under normal circumstances may lead to biased estimates. The results are intriguing. In terms of franchise value, while pooled OLS estimates suggest no copyright impact, feasible GLS models allowing the errors be groupwise heteroskedastic and follow an AR(1) process and the dynamic GMM estimator indicate a robust, negative, and statistically significant copyright effect. Specifically, a logo change reduces franchise value by 5–6%. Finally, while the DID matching estimator yields a similar point estimate (5%), the effect is not statistically significant given the small number of matched pairs. In terms of the copyright effect on consumer demand as measured by tickets sales, the majority of specifications and estimation techniques fail to uncover a statistically significant effect, although the point estimates are consistently positive, in the 5–7% range. The remainder of the paper is organized as follows. Section 2 discusses the data and outlines the empirical methodology. Section 3 presents the results. Section 4 concludes. 2. Data and methodology 2.1. Data The data set includes information on the 31 current NFL franchises and spans the period 1991–2000.1 The value of each franchise in each year is obtained from Forbes Magazine; annual attendance and other franchise attributes are public information. As stated previously, in principal the value of other franchise assets could have been examined as well. For instance, merchandise sales are presumably most directly affected by logo 1
Data limitations prevent us from utilizing data prior to 1991. Moreover, the Houston Texans did not begin play until the 2002–2003 season; thus, only 31 franchises.
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changes (if there is any impact) in professional sports. However, because the NFL mandates revenue-sharing among the franchises for revenue obtained from merchandise sales, television contracts, etc., franchise-specific data on such sources of revenue are not publicly available. Nonetheless, since franchise value reflects all of these underlying revenue streams, as well as accounts for the NFL’s revenue-sharing procedures, if there is a copyright effect, we still expect variation in franchise value to be systematically related to logo changes. Publicly available franchise-specific attributes available as controls are: whether or not the team has changed its logo from the preceding season, annual wins and losses, whether the team won or lost the Super Bowl in a given year, whether the franchise is new or relocated to a new city since the preceding season, the age of the franchise, the conference and division in which the team plays, and stadium capacity. Finally, we also utilize controls for the socio-economic characteristics of each franchise’s home market: population, per capita income, and the local unemployment rate (obtained from the US Bureau of Economic Analysis). Summary statistics, disaggregated by logo changers and non-changers, are provided in Table 1. Over the 10-year period analyzed, we observe 14 logo changes. While additional Table 1 Summary statistics, 1991–2000 Variable
Logo Changers
Franchise value (millions US$) Tickets sold (100,000 s) Franchise age (years) New team (1 ¼ Yes) Relocated team (1 ¼ Yes) Wins (per season) Losses (per season) Super bowl champ (1 ¼ Yes) Super bowl loser (1 ¼ Yes) Stadium capacity (10,000 s) Population (millions) Per capita income (10,000 s US$) Unemployment rate
Non-changers
Mean
Std. dev.
Mean
Std. dev.
273.42
112.75
218.18
117.04
5.28
0.65
4.84
1.24
43.14
15.45
40.38
21.70
0.00
0.00
0.02
0.14
0.00
0.00
0.01
0.08
9.93
2.84
7.90
2.95
6.07
2.84
8.09
2.95
0.07
0.27
0.03
0.17
0.21
0.43
0.02
0.15
6.97
0.66
6.62
1.51
6.44
6.32
4.72
4.81
3.09
0.49
2.67
0.49
4.26
1.67
5.06
1.88
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variation would aid in identifying the copyright effect, as evidenced in the next section, we do not feel the relatively small number of logo changes inhibits one from obtaining a good understanding of the role of copyrights in accounting for the variation in franchise value and ticket sales. In terms of observable differences among franchises that altered their logos and those that did not, several interesting observations arise from Table 1. First, franchises that reinvented their logos were valued at roughly $55 million more than those that did not. However, franchises that reinvented their logo were valued at approximately $57 million more on average than franchises that did not undertake any logo changes the year prior to reinventing their logo. Thus, franchises that are more valuable to begin with are more likely to undertake logo changes. Second, consumer demand measured by ticket sales for franchises with new logos exceeded demand for those that retained previous logos by 44,000 on average; the average difference between soon-to-be logo changers and nonchangers in the year prior to the change was only 21,000. Third, the franchises with new logos were more successful—measured in terms of victories—than those that did not reinvent their logos, winning an average of two additional games per year; in the year prior to the change, the average difference in win total between soon-to-be logo changers and non-changers was 0.3. 2.2. Parametric approach To assess the impact of copyrights on franchise value and ticket sales in a statistical framework, we begin with several standard parametric panel data models. The parametric specifications used to estimate the effect of a logo change on franchise attributes are nested in the following estimating equation: lnðyit Þ ¼ ai þ lt þ dLit þ X it b þ it ,
(1)
where yit is the outcome of interest for franchise i in year t (i.e., franchise value or ticket sales); ai are franchise fixed effects; lt are year fixed effects; Lit is a binary variable taking a value of unity if a franchise changed its logo from the previous year, zero otherwise; Xit is a vector of franchise attributes to be controlled. The variables in X include: previous won/ loss record, controls for whether or not the team won the league championship or made it into the league championship game that year, dummy variables for whether the team is a new franchise or relocated from a different city, the seating capacity of the team’s home arena, and finally socio-economic characteristics of the franchises home metropolitan area (population, mean per capita income, and unemployment rate in that city). The most parsimonious specification we estimate restricts ai ¼ a for all i. This amounts to a simple pooled OLS regression, although we report standard errors that are robust to heteroskedasticity and arbitrary correlation of the residuals within franchises. Next, we relax the assumption that ai ¼ a, and include both franchise and year effects in (1). Again, we report robust standard errors. Third, we again impose the assumption of no franchisespecific heterogeneity, but we explicitly allow the error term to follow an AR(1) process, and for the variance of the residual to be franchise-specific. This is estimated by Feasible Generalized Least Squares (FGLS). Finally, we re-estimate the FGLS model allowing for both franchise- and year-specific effects. Before proceeding, three comments are in order. First, FGLS is more efficient than simply using pooled OLS with robust standard errors if the error structure is well specified.
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If it is not, the pooled OLS with robust standard errors is preferred. Tests of groupwise heteroskedasticity are conducted (Greene, 2000, p. 598). Second, our focus on the potential autoregressive nature of the error terms arises from the fact that unobservables such as fan support are likely to persist over short time periods. Finally, as the final two methods do not rely on the assumption of normality, we also conduct tests for normality of the residuals (Doornik and Hansen, 1994). 2.3. Dynamic panel approach An alternative specification is the dynamic panel model of Arellano and Bond (1991) estimated via the General Method of Moments (GMM). The benefit of this specification is that it explicitly conditions on lagged values of the dependent variable, while also controlling for unobserved franchise-specific heterogeneity. Thus, as opposed to allowing for autocorrelation in unobservable shocks to franchise value and/or ticket sales (e.g., trends in the popularity of the franchise), the model explicitly allows past levels of the outcome of interest to affect current levels. Moreover, as stated in Section 2.1, the decision to reinvent a franchise’s logo is positively correlated with ticket sales and franchise value. The model uses first-differences to remove time-invariant, franchise-specific attributes, and then uses twice-lagged (and higher orders) of the dependent variables as instruments for the lagged values of the dependent variable. Specifically, the model is given by S~ it ¼ ai þ lt þ yS~ it1 þ dLit þ X it b þ it , where S~ is the logarithm of franchise value or ticket sales. First-differencing yields
(2)
DS~ it ¼ Dlt þ yDS~ it1 þ DdLit þ DX it b þ Dit . (3) ~ Assuming the errors, eit, are not autocorrelated, DS it1 will still be correlated with the error term, Dit1 , in (3). However, S~ it2 , S~ it3 , etc. are available as instruments. If, on the other hand, eit is autocorrelated (or, equivalently, Deit follows an AR(2) process or higher), then the instruments will be invalid. Tests of autocorrelation and a Sargan test of the overidentifying restrictions are conducted, as in Arellano and Bond (1991). 2.4. Propensity score matching method An alternative method of assessing the impact of a discrete treatment on an outcome of interest is the method of propensity score matching developed in Rosenbaum and Rubin (1983). While extensively used by statisticians, economic applications have been sparse until recently. A few notable examples include Dehejia and Wahba (1999, 2002), Heckman et al. (1997, 1998), List et al. (2003), and Smith and Todd (2005). Blundell and Costa-Dias (2002) provide an excellent introduction to the matching method, concluding, ‘‘matching methods have been extensively refined in the recent evaluation literature and are now a valuable part of the evaluation toolbox’’ (p. 4). The fundamental problem in identifying treatment effects is one of incomplete information. While the econometrician observes whether the treatment occurs and the outcome conditional on treatment assignment, the counterfactual is unobserved. Let yi1 denote the outcome of observation i if the treatment occurs (given by Ti ¼ 1); yi0 denotes the outcome in the absence of treatment (Ti ¼ 0). If both states of the world were observable, the average treatment effect, t, would equal y1 y0 , where the former (latter)
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average represents the mean outcome for the treatment (control) group. However, given that only y1 or y0 is observed for each observation, unless assignment into the treatment group is random, generally tay1 y0 . The solution Rosenbaum and Rubin (1983) advocate is to find a vector of covariates, Z, such that y1 ; y0 ? TjZ;
prðT ¼ 1jZÞ 2 ð0; 1Þ,
(4)
where ? denotes independence. If one is interested in estimating the average treatment effect, only the weaker condition (40 ) E y0 jT ¼ 1; Z ¼ E y0 jT ¼ 0; Z ¼ E y0 jZ ; prðT ¼ 1jZÞ 2 ð0; 1Þ is required. To implement the matching technique, the treatment group is defined as the set of franchises that changed their logo from the preceding year. The outcome of interest, y, is the (logarithm of) franchise value or ticket sales. For condition (40 ) to hold, the conditioning set Z should be multi-dimensional. Consequently, finding observations with identical values for all covariates in Z may be untenable. However, Rosenbaum and Rubin (1983) prove that conditioning on p(Z) is equivalent to conditioning on Z, where pðZÞ ¼ prðT ¼ 1jZ Þ is the propensity score. p(Z) is estimated via a standard probit model. Upon estimation of the propensity score, a matching algorithm must be defined in order to estimate the missing counterfactual, y0i, for each treated observation i. The simplest algorithm is nearest-neighbor matching, whereby each treated observation is paired with the control observation whose propensity score is closest in absolute value (Dehejia and Wahba, 2002).2 Unmatched controls are discarded and the average treatment effect on the treated (TT) is (5) tTT ¼ E y1 T ¼ 1; pðZÞ E y0 T ¼ 0; pðZÞ ¼ E y1 y0 pðZÞ . The estimator in (5) will provide an unbiased estimate of TT only if condition (40 ) is satisfied. As such, matching is useful as a solution to problems of selection on observables. However, we amend the basic matching algorithm in two important ways to utilize our panel data and remove certain unobservables that may not be controlled by simply conditioning on the propensity score. First, we restrict the pool of potential controls to which a given treated observation may be paired. Specifically, we perform the matching exercise twice: (i) unrestricted matching, and (ii) restricting matched pairs to be from the same year. By matching within-year, we explicitly remove any time-specific unobservables not already controlled for by the propensity score. This is the matching method’s analogy to fixed effects, and is similar to the claims made in Smith and Todd (2005) that matches— used to identify the effect of employment programs—should be from the same labor market. Thus, the estimator in (5) becomes tTT;t ¼ E y1 T ¼ 1; pðZÞ; t E y0 T ¼ 0; pðZÞ; t ¼ E y1 y0 pðZÞ; t , (6) where t indexes year. 2 Typically nearest-neighbor matching is performed with replacement, implying that a given control observation may be matched to multiple treatment observations. Dehejia and Wahba (2002) verify that matching with replacement fares at least as well as matching without replacement and possibly better.
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Second, we employ a difference-in-differences (DID) matching estimator, similar to that used in Eichler and Lechner (2002), Heckman et al. (1997), and List et al. (2003). The strategy entails making an assumption of bias stability (BS) and requires data on both the treated and the controls prior to the treatment date. The idea is that although the condition in (40 ) may not hold due to the presence of unobservables, the bias detected prior to the actual treatment date may provide a reasonable estimate of the post-treatment bias. To see this, consider the method of matching more closely. The average treatment effect on the treated group in (5) is equivalent to tTT ¼ E E y1 T ¼ 1; pðZÞ E y0 T ¼ 1; pðZÞ ¼ E E y1 T ¼ 1; pðZÞ E y0 T ¼ 0; pðZÞ ,
(7) where the outer expectation is over the distribution of Z|T ¼ 1. If the conditional independence assumption in (40 ) does not hold, the bias, B, is given by (8) B ¼ E y0 T ¼ 1; pðZÞ E E y0 T ¼ 0; pðZÞ , where again the outer expectation of the second right-hand side term is over the distribution of Z|T ¼ 1. The bias, B, is estimated by the mean difference in franchise value or ticket sales prior to the treatment and is subtracted from the estimated treatment effect obtained in (5) or (6). For notation, we define the DID counterpart to (5) and (6) as tDID ¼ tTIT t0TT ,
(9a)
tDID;t ¼ tTIT;t t0TT;t ,
(9b)
where t0 TT, t0 TT,t are the mean differences in lagged franchise value or ticket sales across the matched treatment and control groups in the unrestricted and restricted cases, respectively. Upon completing the matching estimation, balancing tests are conducted. Balancing refers to the fact that after conditioning on the propensity score and obtaining the matched sub-sample, the distribution of the conditioning variables, Z, should not differ across the treatment and control group. Thus, after matching, we also test for differences in the mean of the Z’s. Finally, prior to continuing, it is important to highlight the differences between matching estimators and the estimators from the previous section. First, the matching estimator entails relatively few distributional assumptions. Second, matching allows for non-parametric interactions between all the covariates in Z in the determination of the outcome of interest (Bratberg et al. 2002). Finally, matching estimators identify a restricted sub-sample of control observations that are most ‘‘similar’’ to the treatment group, whereas the previous models utilize all available observations. While this may be a positive to the extent that control observations deemed too different from the treatment group are excluded, in applications with few treated observations this leads to small sample sizes. 3. Empirical results 3.1. Parametric estimates Table 2 presents the estimates from the four specifications discussed in Section 2.2. The coefficient estimates of primary interest are displayed in bold. In the interest of brevity, we
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only report the coefficient on logo change (the full set of results are available upon request). Columns 1–4 display the results for franchise value; columns 5–8 present the results for ticket sales. In terms of the copyright impact on franchise value, the simple pooled OLS model with time effects and a no franchise-specific heterogeneity (column 1) indicates that logo changes have a negative, albeit statistically insignificant, impact on franchise value (d^ ¼ 0:02, robust standard error ¼ 0.04). Allowing the intercept to vary by franchise (column 2) yields a similar same result (d^ ¼ 0:03, robust standard error ¼ 0.03), despite the fact that we reject the null of equal intercepts across franchises (F ¼ 7.85, P ¼ 0.00). Columns 3 and 4 present the FGLS results with (column 4) and without (column 3) franchise-specific intercepts. The FGLS models allow for groupwise heteroskedasticity and AR(1) errors. As this imposes a specific structure on the errors, the results are more efficient than the pooled OLS results with robust standard errors if the error structure is correctly specified. As in the pooled OLS models, while we easily reject the null of no franchise-specific heterogeneity (w2 ¼ 158.72, P ¼ 0.00), the copyright effect is virtually ^ ^ unaffected, with the point estimates being d ¼ 0:06 d ¼ 0:05 in column 3 (4). Furthermore, both estimates are statistically significant at the 95% confidence level. The fact that the point estimates of the copyright effect on franchise value are negative, with some even statistically significant, is surprising since, as stated previously, undertaking logo changes is costly and there does not appear to be any motivation to do so unless there is an economic benefit. Thus, we turn to some diagnostic tests of these specifications. First, tests for groupwise heteroskedasticity in the pooled OLS model with franchise-specific effects and both FGLS models clearly reject the null of a constant residual variance across franchises, thus validating our use of robust standard errors or explicit allowance for the variance to vary across franchises. Second, in all four models, the test for normality of the residuals overwhelmingly rejects the null in every case. While this may invalidate hypothesis tests, it does not affect the negative point estimates. Consequently, we examine the robustness of these findings through the use of alternative estimation methods. Prior to examining these additional results, columns 5–8 in Table 2 display the analogous pooled OLS and FGLS results for the impact of copyrights on ticket sales. In all four specifications, the copyright impact is statistically insignificant and the point estimates are extremely close to zero. Thus, we fail to find any influence of logo changes on the demand for NFL franchise output as measured by in-person viewing of games. In terms of the diagnostic tests, the results are similar to those in the models examining for franchise value. Specifically, we find significant evidence of franchise-specific heterogeneity (although such heterogeneity does not affect the estimated copyright effect), groupwise heteroskedasticity, and we consistently reject the null of normality. 3.2. Dynamic panel estimates The results using the Arellano and Bond (1991) GMM estimator are presented in Tables 3 (franchise value) and 4 (ticket sales). For each outcome, four specifications are estimated: (i) conditioning on (one-period) lagged values of the dependent variable; (ii) conditioning on (one-period) lagged values of the dependent variables and measures of franchise success (i.e., wins and Super Bowl victories and defeats); (iii) conditioning on
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Table 2 Parametric estimates of the logo effect Franchise value
Ticket sale
Pooled OLS
Pooled OLS
GLS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.02 (0.04) No
0.03 (0.03) Yes
0.06* (0.02) No
0.05* (0.02) Yes
0.01 (0.03) No
0.01 (0.02) Yes
0.00 (0.01) No
2.3 1003 (0.01) Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
w2(9) ¼ 693.80 (P ¼ 0.00) w2(28) ¼ 158.72 (P ¼ 0.00)
F(9, 274) ¼ 1.05 (P ¼ 0.43)
F(9, 274) ¼ 2.02 (P ¼ 0.07) F(30, 244) ¼ 11.22 (P ¼ 0.00) w2(31) ¼ 7.4*1026 (P ¼ 0.00)
w2(9) ¼ 6.53 (P ¼ 0.69)
w2(9) ¼ 8.14 (P ¼ 0.52) w2(29) ¼ 327.10 (P ¼ 0.00)
w2(31) ¼ 5.9*1006 (P ¼ 0.00)
w2(30) ¼ 2.2*1024 (P ¼ 0.00)
w2(2) ¼ 110.09 (P ¼ 0.00) 294
w2(2) ¼ 364.40 (P ¼ 0.00) 294
w2(2) ¼ 118.24 (P ¼ 0.00) 294
F(9, 270) ¼ 48.15 F(8, 241) ¼ 43.69 w2(9) ¼ 780.82 (P ¼ 0.00) (P ¼ 0.00) (P ¼ 0.00) F(30, 241) ¼ 7.85 (P ¼ 0.00)
w2(2) ¼ 53.16 (P ¼ 0.00) 291
w2(31) ¼ 3220.75 (P ¼ 0.00)
w2(30) ¼ 1270.46 (P ¼ 0.00)
w2(30) ¼ 1945.38 (P ¼ 0.00)
w2(2) ¼ 30.44 (P ¼ 0.00) 291
w2(2) ¼ 85.75 (P ¼ 0.00) 290
w2(2) ¼ 24.38 (P ¼ 0.00) 290
w2(2) ¼ 163.38 (P ¼ 0.00) 294
Notes: Each specification also includes controls for: franchise age, number of wins, whether the team won the league championship, whether the team lost in the league championship, arena capacity, total ticket sales, and the population, unemployment rate, and mean per capita income of the franchise’s home metropolitan area. GLS models allow for groupwise heteroskedasticity and AR(1) errors, with a common correlation coefficient. Standard errors or P-values in parentheses; standard errors in pooled OLS models are robust to arbitrary heteroskedasticity and correlation within franchises. Test for groupwise heteroskedasticity based on Greene (2000, p. 598). Omnibus test for normality based on Doornik and Hansen (1994). *Indicates significant at 5% level. **Indicates significant at 10% level.
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Logo change (1 ¼ Yes) Franchise Effects Year Effects Joint significance of year effects Joint significance of Franchise effects Modified Wald test for groupwise heteroskedasticity Omnibus test for normality Observations
GLS
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Independent variable
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one-period lagged values of the dependent variables and one- and two-period measures of franchise success; and, (iv) conditioning on one- and two-period lagged values of the dependent variables and measures of franchise success. All specifications also include controls for the contemporaneous values of the remaining franchise attributes. In addition to reporting the most relevant coefficient estimates, we also report the results of the Sargan overidentification test and the test for no autocorrelation (in the non-differenced data). All four specifications in Table 3 find a negative and statistically significant (at the 95% confidence level) effect of logo changes on franchise value. Specifically, as in the FGLS models in Table 2 that explicitly allowed for autocorrelation, a logo change is associated with an average decline in franchise value of 5–6%. Moreover, franchise value is found to be highly persistent over time as lagged values are positively related to current value, as one would expect. Finally, the Sargan test and test for no autocorrelation indicate that all models are well specified with regards to the validity of the instruments and the assumptions concerning the errors. In terms of ticket sales, Table 4 reports a consistent point estimate of 0.05–0.06 across the four specifications; however, only the estimate in column 1 is statistically significant at the 90% level. While the specifications in columns 2–4 find a similar logo effect as in Table 3 GMM estimates of the logo effect on franchise value Independent variable Logo change (1 ¼ Yes) Lagged ln(value) Twice-lagged ln(value) Lagged Success Variables Twice-lagged Success Variables Franchise Effects Year Effects Joint significance of year effects Sargan Over identification Test Ho: No autocorrelation
(1)
(2) *
(3) *
(4) *
0.05 (0.02) 0.26** (0.14) —
0.06 (0.02) 0.29* (0.14) —
0.06 (0.02) 0.35* (0.15) —
No
Yes
Yes
0.06* (0.02) 0.51* (0.16) 0.10 (0.07) Yes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
w2(7) ¼ 331.11 (P ¼ 0.00) w2(35) ¼ 9.60 (P ¼ 1.00)
w2(6) ¼ 253.36 (P ¼ 0.00) w2(35) ¼ 9.57 (P ¼ 1.00)
w2(6) ¼ 305.36 (P ¼ 0.00) w2(35) ¼ 7.90 (P ¼ 1.00)
w2(6) ¼ 246.03 (P ¼ 0.00) w2(33) ¼ 5.82 (P ¼ 1.00)
P ¼ 0.22
P ¼ 0.20
P ¼ 0.21
P ¼ 0.45
Notes: Each specification also includes controls for: number of wins, whether the team won the league championship, whether the team lost in the league championship, arena capacity, and the population, unemployment rate, and mean per capita income of the franchise’s home metropolitan area. ‘‘Success variables’’ include wins and dummy variables indicating that the team either won the league championship or lost in the league championship. Robust standard errors or P-values in parentheses. *Indicates significant at 5% level. **Indicates significant at 10% level.
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Table 4 GMM estimates of the logo effect on ticket sales Independent Variable Logo change (1 ¼ Yes) Lagged ln(ticket sales) Twice-lagged ln(ticket sales) Lagged Success Variables Twice-lagged Success Variables Franchise Effects Year Effects Joint significance of year effects Sargan Over identification Test Ho: No autocorrelation
(1)
(2)
(3)
(4)
0.06** (0.04) 0.52* (0.13) — (0.14) No
0.06 (0.04) 0.46* (0.14) —
0.06 (0.04) 0.43* (0.15) —
0.05 (0.04) 0.44* (0.15) 0.11
Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
w2(7) ¼ 11.65 (P ¼ 0.11) w2(35) ¼ 5.08 (P ¼ 1.00)
w2(6) ¼ 8.04 (P ¼ 0.24) w2(35) ¼ 6.11 (P ¼ 1.00)
w2(6) ¼ 8.21 (P ¼ 0.22) w2(35) ¼ 2.46 (P ¼ 1.00)
w2(6) ¼ 7.28 (P ¼ 0.30) w2(33) ¼ 3.75 (P ¼ 1.00)
P ¼ 0.90
P ¼ 0.93
P ¼ 0.98
P ¼ 0.53
Notes: See Table 3.
column 1, the standard errors increase sufficiently such that the logo effect is no longer statistically significant at conventional levels. Finally, as in Table 3, all four specifications fair well in terms of the Sargan test and test for no autocorrelation, as well as find a positive and statistically significant effect of lagged values of the dependent variable as one would expect if fan loyalty and season ticket sales change slowly over time. 3.3. Propensity score matching estimates The final estimation technique is the semi-non-parametric propensity score matching method. The results are shown in Table 5. Column 1 (2) shows the mean differences between the matched treatment (logo changers) and control group (logo non-changers) using the unrestricted (within-year) matching algorithm. The average difference in the propensity score across the matched pairs is 0.05 with unrestricted matching; 0.10 under within-year matching. Neither difference is statistically significant (unrestricted: P ¼ 0.54; within-year: P ¼ 0.22). In addition, prior to discussing the various estimates of the treatment effects, we note that the differences between the matched treatment and control group in terms of the various observed attributes are never statistically significant at the 95% confidence level. Moreover, we never reject the null of joint equality of the means of the various control variables using a Hotelling T2-tests (unrestricted matching: F ¼ 0.38, P ¼ 0.96; within-year matching: F ¼ 0.34, P ¼ 0.97).
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Table 5 Propensity score estimates of the logo effect Independent variable
Propensity score ln(value) (tTT,K) Lagged value D ln(value) (tDID,) ln(ticket sales) (tTT,) Lagged ticket Sales D ln(ticket sales) (tDID,) Wins Super bowl champion (1 ¼ Yes) Super bowl loser Population (millions) Unemployment Rate (0-100) Per capita Income (1000 s) Franchise age (years) Stadium Capacity (1000 s) AFC east (1 ¼ Yes) AFC central (1 ¼ Yes) AFC west (1 ¼ Yes) NFC east (1 ¼ Yes) NFC central (1 ¼ Yes) NFC West (1 ¼ Yes) Hotelling T2 Number of Matched pairs Number of Unique controls
Matching algorithm Unrestricted (1)
Within-year (2)
0.05 (P ¼ 0.54) 0.23 (P ¼ 0.19) 0.26 (P ¼ 0.11) 0.03 (P ¼ 0.52) 0.05 (P ¼ 0.37) 0.06 (P ¼ 0.43) 0.11 (P ¼ 0.06) 0.43 (P ¼ 0.66) 0.07 (P ¼ 0.33) 0.00 (P ¼ 1.00) 1.02 (P ¼ 0.67) 0.51 (P ¼ 0.52) 0.80 (P ¼ 0.72) 4.21 (P ¼ 0.40) 0.86 (P ¼ 0.80) (1) 0.36 (P ¼ 0.06) 0.14 (P ¼ 0.30) 0.00 (P ¼ 1.00) 0.07 (P ¼ 0.56) 0.00 (P ¼ 1.00) 0.14 (P ¼ 0.30) F(14, 13) ¼ 0.38 (P ¼ 0.96) 14
0.10 (P ¼ 0.22) 0.02 (P ¼ 0.91) 0.03 (P ¼ 0.86) 0.05 (P ¼ 0.19) 0.06 (P ¼ 0.29) 0.01 (P ¼ 0.94) 0.07 (P ¼ 0.22) 0.50 (P ¼ 0.63) 0.00 (P ¼ 1.00) 0.14 (P ¼ 0.30) 0.92 (P ¼ 0.67) 0.78 (P ¼ 0.15) 0.65 (P ¼ 0.74) 5.50 (P ¼ 0.38) 1.32 (P ¼ 0.61) (2) 0.07 (P ¼ 0.68) 0.07 (P ¼ 0.64) 0.07 (P ¼ 0.56) 0.07 (P ¼ 0.64) 0.00 (P ¼ 1.00) 0.00 (P ¼ 1.00) F(14, 13) ¼ 0.34 (P ¼ 0.97) 14
12
12
Notes: Parameter estimates refer to the mean difference between the matched treatment and control group, where observations in the control group are weighted by the number of times they appear. P-values are associated with the null that the means are equal across the treatment and control groups. ‘‘Unique controls’’ reports the number of controls that are matched with at least one treatment observation.
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In terms of the estimated copyright effect on franchise value, the franchise value of teams that reinvented their logos exceeds the value of those that did not by 23% on average using the unrestricted matching algorithm, although the difference is not statistically significant (P ¼ 0.19). However, as stated previously, if assignment to the treatment group is based on unobservables and these unobservables are associated with franchise value, then the matching estimate of the average treatment effect will be biased. Thus, we turn to the DID estimator. Here, we see that the lagged franchise value of logo changers exceeds that for logo non-changes by 26% (although this difference is not statistically significant; P ¼ 0.11). Consequently, the DID estimate of the average treatment effect is 3%. While not statistically significant given the availability of only 14 matched pairs (P ¼ 0.52), the point estimate differs very little from those reported in Tables 2 and 3 by the previous econometric methods. Although not discussed previously, in Tables 2 and 3 we always reject the null of no time effects. Given the importance of the time effects in explaining franchise value, the withinyear matching estimators are preferred. Examining the within-year matching results shows that while the average differences in current and lagged franchise value across logo changers and non-changers are vastly different than those obtained by the unrestricted matching (although both remain statistically insignificant), the preferred DID estimate is virtually unchanged, suggesting that logo changers suffer a change in franchise value of 5% (P ¼ 0.19). Thus, matching within-year and utilizing the DID approach yields an estimate that is nearly identical to those displayed in Tables 2 and 3, with the lack of statistical significance reflecting the fact that the matching estimates are based on a smaller sample size as unmatched controls are discarded. Nonetheless, the negative copyright effect on franchise value is robust across all methodologies and modeling assumptions. In terms of ticket sales, the unrestricted and within-year matching finds that logo changers have 5–6% greater ticket sales than logo non-changers on average. Moreover, lagged ticket sales for non-changers exceed that for changers by 1–6%. Thus, the DID estimates of the copyright effect on consumer demand as measured by ticket sales is 11% (7%) according to the unrestricted (within-year) matching, with the unrestricted matching estimate being statistically significant at the 90% confidence level despite the small sample size (P ¼ 0.06). Moreover, since the null of no time effects is not rejected at the 95% confidence level in all specifications in Tables 2 and 4, the unrestricted matching estimates are preferred as unrestricted matching allows matched pairs that have more similar propensity scores. Overall, then, the various methodologies suggest a less robust, but positive, copyright effect on consumer demand. 4. Concluding remarks This paper analyzed the impact of copyrights on firm values and on the demand for firm output. The copyright in question is logos of professional football teams in the United States. Using several parametric estimators, the Arellano and Bond (1991) dynamic panel estimator, and a semi-non-parametric method based on difference-in-differences propensity score matching, we find a negative and statistically significant impact on franchise value, robust across most methodologies, and at best a marginally significant positive impact on ticket sales. Given that the invention of new logos is costly and there does not appear to any benefit of undertaking a logo change that should not be incorporated into the value of the franchise (e.g., merchandise sales, fan appeal, appeal to players, etc.), the
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negative effect on franchise value is particularly startling. Moreover, if franchise value incorporates consumer demand, then not only is there a net negative effect of logo changes on franchise value, but logo changes must result in some negative effects that more than offset the (marginal) positive effect on ticket sales. As this is the first empirical study, to our knowledge, attempting to quantify the impact of copyrights on firms, clearly future research into the understanding what these negative effects are, and if other forms of copyrights yield similar negative impacts, is warranted. Acknowledgments The authors thank Michael McAleer, two anonymous referees, and participants at the Australasian Meeting of the Econometric Society, July 2002, for helpful comments and suggestions. References Arellano, M., Bond, S., 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297. Blundell, R., Costa-Dias, M., 2002. Alternative approaches to evaluation in empirical microeconomics. Portuguese Economic Journal 1, 91–115. Bratberg, E., Grasdal, A., Risa, A.E., 2002. Evaluating social policy by experimental and nonexperimental methods. Scandanavian Journal of Economics 104, 147–171. Dehejia, R.H., Wahba, S., 1999. Casual effects in nonexperimental studies: reevaluating the evaluation of training programs. Journal of the American Statistical Association 94, 1053–1062. Dehejia, R.H., Wahba, S., 2002. Propensity score matching for nonexperimental causal studies. Review of Economics and Statistics 84, 151–161. Doornik, J.A., Hansen, H., 1994. An omnibus test for univariate and multivariate normality. Unpublished manuscript, Nuffield College, Oxford University. Eichler, M., Lechner, M., 2002. An evaluation of public employment programmes in the East German state of sachsen-anhalt. Labour Economics 9, 143–186. Greene, W., 2000. Econometric Analysis. Prentice-Hall, Upper Saddle River, NJ. Heckman, J.J., Ichimura, H., Todd, P.E., 1997. Matching as an econometric evaluation estimator: evidence from evaluating a job training program. Review of Economic Studies 64, 605–654. Heckman, J.J., Ichimura, H., Todd, P.E., 1998. Matching as an econometric evaluation estimator. Review of Economic Studies 65, 261–294. Lanjouw, J.O., Pakes, A., Putnam, J., 1998. How to count patents and value intellectual property: uses of patent renewal and application data. Journal of Industrial Economics 46, 405–433. List, J.A., Millimet, D.L., Fredriksson, P.G., McHone, W.W., 2003. Effects of environmental regulations on manufacturing plant births: evidence from a propensity score matching estimator. Review of Economics and Statistics 85, 944–952. Pakes, A., 1985. On patents, R and D, and the stock market rate of return. Journal of Political Economy 93, 390–409. Pakes, A., 1986. Patents as options: some estimates of the value of holding European patent stocks. Econometrica 54, 755–784. Rosenbaum, P., Rubin, D., 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41–55. Schankerman, M., Pakes, A., 1986. Estimates of the value of patent rights in European countries during the post1950 period. The Economic Journal 96, 1052–1076. Smith, J., Todd, P.E., 2005. Does matching address lalonde’s critique of nonexperimental estimators. Journal of Econometrics 125, 305–353.