JSTOR

A. Econometric Model

As shown in table 1, during a new stadium’s debut season, revenue and attendance increase very substantially. Relative to the final season in the old stadium, revenue and attendance during the first year in a new stadium are on average higher by 47.0% and 33.5%, respectively. By comparison, for all seasons and teams in the sample, the means of the corresponding annual increases are only 7.35% and 1.2%. Hence, compared to a typical season, teams playing in new stadiums enjoyed revenue higher by 37% and attendance higher by 32%. These figures strongly suggest that stadium construction has significant effects on demand for baseball. The specific figures, however, cannot be taken too literally since the unconditional means do not account for the many nonstadium factors that affect baseball demand. Furthermore, there remains the question of how well the demand boost holds up over subsequent seasons. For instance, during a stadium’s first season, the stadium’s novelty attracts many inquisitive patrons. But casual observation indicates that during subsequent seasons attendance declines somewhat, perhaps because novelty wears off. This phenomenon has been dubbed the “honeymoon effect” (Hamilton and Kahn 1997). To estimate such dynamic effects and to control for nonstadium factors are the purposes of our econometric models. Demand for baseball depends on numerous factors, many of which can be difficult to identify or quantify. Our fixed‐effects models offer the advantage of implicitly controlling for the effects of all unspecified factors to the extent that they are either time specific (vary only over time, not across teams) or team specific (vary only across teams, not over time).

Undoubtedly, factors that vary only over time or only across teams, or those that vary predominantly across either time or teams, do account for a substantial fraction of variation in team revenues. For instance, an important time‐specific factor is the players’ strike that caused cancellation of the 1994 World Series. The strike soured many fans, at least temporarily, so that when play resumed in 1995, attendance dropped significantly. After 1995, attendance resumed a long‐term growth trend. Indeed, the trend itself is another important time‐specific effect. The significance of the trend is reflected in the facts that mean team attendance was 15% higher in 2001 than in 1990 and mean revenue was 126% higher. Part of the revenue increase is attributable to inflation, another significant time‐specific effect. As for team‐specific effects, examples include the management expertise of the franchise (Goff, McCormick, and Tollison 2002) and differences in various attributes of home cities, including population (e.g., Kansas City vs. New York), local preferences, availability of substitute forms of entertainment, transportation costs, per capita income, and conceivably even the outdoor climate. These considerations underscore the importance of employing fixed‐effects models. By controlling for team‐ and time‐specific factors, the fixed‐effects models help to avert omitted variable bias and to thereby secure consistent estimates of the effects of stadium construction.3

We estimate our revenue model using 308 annual observations spanning the years 1991–2001 and including all major league teams.4 The model takes the following form: The dependent variable, REV_i,t, is the log of total revenue for team i in year t. To account for the effect of stadium novelty, or the honeymoon effect, the model includes a dummy indicator, FIRST_i,t, that takes the value one if team i opens a new stadium in season t; otherwise FIRST_i,t equals zero. To capture any long‐term or permanent revenue effect, the model also features a dummy indicator, NEW_i,t, that takes the value one if team i opens a new stadium in period t and remains equal to one for all subsequent seasons. Since attendance might be constrained by stadium size, the variable CAP_i,t represents the log of seating capacity.

The model also includes some control variables unrelated to characteristics of stadiums. The variable WIN_i,t represents team i’s proportion of games in season t that it won; this variable measures team quality. Our model also features a variable for ticket price. To avoid potential simultaneity, we use posted prices that are determined prior to the start of the season. These prices are not endogenous with respect to attendance or revenue because they are predetermined.5 For reasons discussed in Section III, we focus on the price of a so‐called reserved seat. Hence, our price variable, PRICE_i,t, equals the log of the posted price for a particular subcategory of reserved seating.6

Our model also allows stadium construction to affect the elasticity of revenue with respect to team performance. To this end, the model includes terms interacting WIN_i,t with the new stadium variables, FIRST_i,t and NEW_i,t. In addition, the model includes a lagged dependent variable to allow for persistence in revenue; in other words, we specify a partial adjustment model. The partial adjustment model acknowledges that consumers might adjust their baseball spending slowly. For example, substitute forms of entertainment might involve search costs or the honeymoon effect might last longer than a single season. Furthermore, consumers might base their perception of team quality on prior performance, not just current performance. This consideration is particularly relevant since a substantial fraction of revenue derives from ticket sales in advance of the start of the season. To account for a potential impact from past performance, the explanatory variables include a lagged value of win proportion, WIN_i,t−1. Finally, to complete the specification of (1), note that γ₀, γ₁, …, γ₈ are coefficients to be estimated, ε_1i,t is a mean zero random disturbance, and g_i and g_t denote, respectively, the team‐specific and time‐specific fixed effects.

The model in (1) implies a specific functional form for the impact of stadium construction. The impact function for the first year is obtained by setting the new‐stadium dummies in (1) to one and subtracting from (1) the same function with the dummies set to zero. Normalizing in the ballpark’s first year, the impact function takes the form where ΔREV_i,0 is the change in log revenue attributable to the new ballpark. The model’s lagged dependent variable causes the impact function for each subsequent season to depend in part on the impact during the previous season: where ΔREV_i,n represents the impact during the nth season subsequent to the stadium’s debut season. (Note that the “Δ” refers not to first‐differences in time but rather to differences across stadium regimes.) Repeated substitution back to the debut season yields the general form of the impact function: The first term on the right‐hand side generates a temporary impulse that dies out exponentially over time and depends on the value of γ₀, the coefficient of the lagged dependent variable. The second term contributes a steady‐state effect to which the impact converges in the long run. Assuming an expected win proportion equal to 1/2, the constant league‐wide average, and taking the limit n → ∞, we obtain the steady‐state impact, ΔREV_SS: The model’s estimation is discussed in the following subsection.

B. Estimates

Our data’s dual time‐series and cross‐sectional nature creates the potential for both heteroscedasticity and serial correlation. We find that our estimated models do not appear to suffer from serial correlation, and this result can be attributed to the apparent ability of the lagged dependent variable and lagged win proportion to account for the persistence in the data. Applying Breusch‐Pagan tests, however, does reveal considerable evidence of heteroscedasticity (see table 2). Consequently, we compute the standard errors of our coefficient estimates using a heteroscedasticity‐consistent covariance matrix.7

Table 2 Fixed‐Effects Models of the Determinants of Team Revenue, Annual Observations, 1991–2001

Open New Window

Column 1 of table 2 presents OLS estimates of equation (1), with team‐ and time‐specific effects accounted for using a least‐squares dummy‐variable method. As table 2 shows, all the model’s control variables except stadium capacity achieve statistical significance at the .05 level. But, as for our primary variables of interest—the four stadium variables, FIRST_i,t, , NEW_i,t, and —none has an estimated coefficient that individually differs significantly from zero. The lack of individual significance, however, belies the variables’ joint significance. In particular, the Wald chi‐square statistic for the joint significance of the four stadium variables is 54.8, which far exceeds the .01 critical value of 13.3. Also, the impact function’s two components—the first‐year effect ΔREV_i,0 and the steady‐state impact ΔREV_SS—each prove to be significantly positive. Using (5) and setting WIN_i,0 in (2) equal to the win proportion’s expected value of 1/2, we compute point estimates of ΔREV_i,0 and ΔREV_SS. The point estimates appear in table 3, along with p‐values corresponding to one‐tailed tests of null hypotheses that each point estimate is nonpositive. As shown in the table’s column 1, the estimated impacts are not only statistically significant but also are rather large in magnitude. The estimated first‐year effect implies an increase in log revenue equal to .288, which is significantly positive at better than the .01 level, while the estimated steady‐state increase in log revenue equals .226, which is significantly positive at about the .02 level. The estimates remain large and statistically significant at other plausible win proportions. At a rather low win proportion of .400, the first‐year and steady‐state estimates become slightly less large, respectively, .278 and .187, while at a quite high win proportion of .600 they are larger, respectively, .296 and .266.

Table 3 Estimates of a New Ballpark’s Impact on Logs of Revenue and Attendance

Open New Window

Clearly, the stadium variables exhibit considerable joint significance despite their insignificance individually. So why do the individual and joint inferences conflict? Statistically, it must be that the revenue series does not contain sufficient information to distinguish between the variables’ individual effects, given the collinearity between them.8 The presence of multicollinearity, however, does not necessarily have adverse implications for our primary objective of predicting the revenue effect of ballpark construction. Researchers typically respond to multicollinearity by deleting some collinear explanatory variables, yet a cogent argument exists for retaining all variables in order to avert model misspecification. This argument is especially pertinent when the primary interest is prediction and the individual variable coefficients are only of secondary interest. Nonetheless, to demonstrate robustness and to be sure that multicollinearity does not impair the precision of our forecasts, we estimate a version of (1) that is pared down to reduce multicollinearity. Thus column 2 of table 2 presents estimates of a version of (1) that omits the capacity variable and the win‐interaction terms, variables that proved individually and jointly insignificant in the full model. This model implicitly assumes a win‐elasticity of revenue that is constant across stadiums, in other words an impact of new stadiums on revenue that is independent of wins. The resulting estimates show that reducing the collinearity enables the two remaining stadium variables (FIRST_i,t and NEW_i,t) to attain statistical significance at better than the .01 level. The implied first‐year and steady‐state effects, displayed in column 2 of table 3, are significantly positive, and in fact they are somewhat larger than those obtained from the full model.9

C. Estimates in First Differences

As noted, the lagged dependent variable plays a key role in modeling the data’s time dependence and contributes considerable explanatory power. In the context of a fixed‐effects model, however, the presence of the lagged dependent variable raises a particular econometric issue. It turns out that the estimated coefficient of the lagged dependent variable, γ₀, converges to the true value, γ₀, only as the number of time periods becomes large, T → ∞, not as the number of cross‐sectional units (teams) becomes large, N → ∞. In other words, the estimate of γ₀ (unlike that of the model’s other coefficients, γ₁, γ₂, γ₃, …, γ₈) is consistent only on T, not on N. Our revenue and attendance models have, respectively, and While not trivial, the T values are nonetheless modest, and so we can expect our estimates of γ₀ to exhibit downward bias, the familiar Hurwicz bias associated with an autoregressive coefficient (Nerlove 1971). But the Hurwicz bias, like multicollinearity, is relatively unlikely to adversely affect prediction. The predictions involve not only γ₀ but also several other coefficients that provide scope for offsetting the influence of any individual coefficient. To demonstrate robustness, however, it is desirable to verify that our predictions are not unduly sensitive to the method used to estimate γ₀.

Following Anderson and Hsiao (1982) and Arellano (1989), we estimate equation (1) in first differences (to account for the team‐specific effects by eliminating them) and use the second lag of the dependent variable, REV_i,t−2, as an instrument for the first difference of the lagged dependent variable, ( ). The resulting two‐stage least‐squares estimate of the coefficient of the lagged dependent variable is consistent on both T and N, not just T. This gain in large sample consistency, however, comes at a price, since some information contained in the levels is discarded by differencing. Furthermore, the use of an instrument creates a source of additional statistical noise. Hence, in a finite sample, the two‐stage procedure is not necessarily superior to ordinary least squares but merely provides an alternative method of pursuing consistent estimation.

Column 3 of table 2 displays two‐stage least‐squares estimates of the differenced model. The resulting estimate of γ₀ is now significantly larger, perhaps reflecting downward bias in the OLS estimates. The new estimate of γ₀ also has a standard error that is approximately three times larger than the corresponding OLS standard error. This increase in the standard error is no doubt attributable to the differenced model’s additional sources of variation. Once again the multicollinearity precludes finding any significant individual coefficients among the stadium variables (despite dropping the capacity variable), and so it is difficult to draw any conclusions without computing the first‐year and steady‐state effects. These appear in column 3 of table 3. At the expected win proportion, the estimated first‐year effect is significantly positive and equal to .253. This essentially concurs with the results of the models in levels. But contrary to the results of the levels models, the differenced model yields an estimated steady‐state effect that is negative, although it is not statistically significant.

The estimates of the differenced model imply that we cannot reject the hypothesis that the steady‐state effect equals zero.10 Of course, this does not mean that a new stadium’s revenue impact immediately reverts to zero. The significant first‐year revenue effect creates an impulse that is propagated through time by the model’s lagged dependent variable. In fact, the lagged dependent variable’s coefficient γ₀ suggests considerable persistence, since its point estimate (.93) is relatively close to one. Furthermore, since γ₀ and the steady‐state effect serve as alternate sources of time persistence, underestimation of γ₀ would tend to coincide with overestimation of the steady state. Hence, it is not surprising that, relative to the levels models, the differenced model should estimate both a higher γ₀ and a lower steady state. And to the extent that these differences offset each other, the differenced and levels models can yield similar forecasts of the revenue effect, given a sufficiently finite horizon. To verify this, however, requires using the estimates to compute predictions at various horizons. We turn to this task in the following subsection.

D. Predictions from Revenue Models

In this subsection, we use estimates of our revenue model (1) to derive predictions of the aggregate revenue effect over various horizons. Recall that during the nth season subsequent to the stadium’s debut season, the effect on log revenue is given by (4). To convert the prediction from (4) into dollars, take the antilog and multiply by REV$₋₁, the dollar value of team revenue for a typical team in the absence of a new stadium. To simplify, assume that REV$₋₁ is constant and set WIN_i,t equal to the constant league‐wide average of 1/2. Then the dollar value of the revenue impact during season n, ΔREV$_n, takes the form Let r represent the (constant) real discount rate. Then the present value of the revenue impact aggregated over the new stadium’s first M seasons is given by Pursuing an analytic solution of the mean and standard error of (7) quickly becomes intractable. Hence, we estimate ΔREV$PV_M via simulation. To calibrate the simulation, assume the following: The assumed value of REV$₋₁ corresponds closely to the median 2001 revenue for teams playing in “old” stadiums.11 Although baseball revenue has for many years consistently grown faster than inflation, we make the rather conservative assumption that REV$₋₁ does not experience future growth. The assumed discount rate of 4% approximately equals the historical average of the real after‐tax yield on corporate bonds.

Let denote a vector whose elements consist of the five parameters in (7): γ₀, γ₁, …, and γ₄. We assume that follows a multivariate normal distribution with mean vector equal to the point estimates— —obtained from the estimated fixed‐effects model. Similarly, let have covariance matrix equal to the relevant 5 × 5 submatrix of the heteroscedasticity‐consistent covariance matrix of fixed‐effects estimates, . We apply a Cholesky decomposition to , and this enables us to generate 5,000 realizations of by simulating random draws from the normal distribution.12 The realizations of yield 5,000 predictions for ΔREV$PV_M by way of (7).

Consider, first, the full model in levels, whose estimates appear in column 1 of table 2. Using these estimates and our simulation procedure, we obtain revenue projections at various horizons, M. The resulting mean predictions appear in column 1 of table 4. Evidently, the projected revenue is considerable, and it quickly makes up a fairly large fraction of the cost of a new ballpark. The first season alone generates expected additional revenue equal to $33 million, or about 12% of the median real cost of the new ballparks in our sample (see table 1). Four additional seasons increase the present value of predicted revenue by an additional $100 million. The five‐season estimate of $133 million amounts to about half the median cost of $268 million. The expected revenue effect surpasses the median cost after only 12 seasons. And 12 seasons would indeed make for a swift recouping of costs, since the expected useful life of a stadium and the duration of a typical lease agreement spans 30–40 seasons. After 20 seasons, our mean revenue prediction exceeds the median cost by more than $100 million, and after 30 seasons it does so by more than $200 million.

Table 4 Present Value of Estimated Revenue Effect at Various Horizons (Million $)

Open New Window

Of course, we must consider not just the means of the revenue simulations but also their standard errors. In fact, as the forecast horizon increases, the standard error grows rapidly. For the first season, the standard error equals $5.3 million, through five seasons it grows to $38 million, and after 30 seasons, it reaches $196 million. These standard errors, however, cannot be used to derive t‐ratios, since (7) is nonlinear, and therefore the realizations of REV$PV_M have a nonstandard distribution. Fortunately, we can use our sample of revenue simulations to directly compute confidence intervals. Hence, for each horizon, table 4 presents the low endpoint for a one‐sided 90% confidence interval, that is, the value above which 90% of the simulated values lie. The resulting low endpoints lie at about half the median stadium cost after 10 seasons; after 30 seasons, the endpoint equals $239 million, or about 90% of the median cost. Thus, the revenue model in levels implies that new ballparks probably do generate sufficient revenue to pay for themselves.

Using our models to project revenue as far as 30 years, however, is a bit fanciful. After all, our revenue data cover only 11 seasons, and we have an average of about five or six annual observations on each new stadium. Therefore, for the sake of argument, let us forbear from extending the model forecasts any further than five seasons. Furthermore, for seasons subsequent to the fifth season, let us err if we must on the side of understating revenue by assuming a rather minimal revenue effect. Specifically, assume that after five seasons a new ballpark’s only remaining source of additional revenue is premium seating.

A distinctive feature of modern stadiums is that architecturally they are designed to accommodate abundant premium seating (Gessing 2001). Marketed to an elite, typically corporate, clientele, premium seating such as luxury boxes and full‐service “club” seats are often cited as the raison d’être of new stadium construction.13 Many other revenue‐enhancing features of new stadiums, such as novelty and cleanliness, can diminish or disappear over time; indeed, let us make the rather gloomy assumption that such features yield no additional revenue after merely five seasons. Premium seating, however, provides a salient, and we assume sole, source of additional revenue that is permanent (after all, the luxury boxes should continue to provide air‐conditioned comfort during the full 30 seasons).

Assume that, relative to an old ballpark, a typical new ballpark is designed to accommodate an additional 50 luxury boxes and 2,500 club seats. Conservative estimates of additional annual revenues would be $50,000 per luxury box and $1,000 per club seat.14 The total gain from premium seating thus amounts to $5 million per season. Aggregating over seasons 6–30 yields a present value equal to $67 million. Adding the estimate of $133 million from the first 5 years brings the total present value to $200 million. This figure accounts for three‐fourths the cost of the median new ballpark and almost fully covers the cost of two of the ballparks in our sample. Even if the true 5‐year total lies at the low endpoint of the 90% confidence interval, total revenue still amounts to $156 million, or about 60% of the median cost. This suggests that new ballpark construction yields internal benefits that, at the very least, cover the lion’s share of the cost of construction.

Table 4 also presents simulated revenue projections derived from the two‐stage least‐squares estimates of the revenue model in first differences.15 As shown in column 2 of table 4, the confidence intervals are considerably wider than those derived from the levels model, to the extent that the low endpoints start to decline after two seasons and become negative after four seasons. The widening of the confidence intervals arises from the differenced model’s relatively large standard errors, particularly that of the coefficient of the lagged dependent variable. This result highlights the fact that, despite asymptotic consistency, in a finite sample the differencing procedure is not necessarily preferable to estimation in levels. At any rate, the differenced model’s mean predictions do nothing to contradict those of the levels model. The differenced model’s mean predictions are somewhat smaller but roughly comparable to those of the levels model. The differenced model predicts a revenue effect of $29 million during the first season and $106 million after five seasons, and these figures are reasonably close to the $33 million and $133 million predictions of the levels model.

A. Econometric Model

We obtain additional revenue estimates by using data on attendance and ticket prices. These data provide a useful source of additional evidence for several reasons. For one, the attendance data might be more reliable than the revenue data, since revenue data can be subject to creative accounting. Also, the estimates from the revenue models cannot be considered definitive since, as with any model, there always exists the possibility of specification error. Furthermore, the attendance and price data have the advantage of being available for earlier seasons. This enables us to consider a larger sample period, 1989–2001, which includes one additional new stadium (Toronto’s Skydome). Estimating separate models of attendance and prices also reveals the relative roles of price and quantity (attendance) in producing the overall revenue effect. Finally, the attendance models allow us to make inferences regarding some ancillary hypotheses, such as the impact of new ballparks on the elasticity of baseball demand with respect to team performance.

We start by estimating our fixed‐effects model in the levels using the least‐squares dummy‐variable method. The data consist of 360 annual team observations from 1989–2001. Since attendance, like revenue, depends on the factors that determine baseball demand, such as team performance and stadium quality, our fixed‐effects model of attendance is entirely analogous to our revenue model. The dependent variable now becomes the log of per game attendance, and among the explanatory variables we continue to include a lagged dependent variable. The remaining explanatory variables are identical to those used in the revenue model and are motivated by equivalent reasoning. Hence, the model takes the following form: where β₀, β₁, …, β₈ are coefficients to be estimated, ε_2i,t is a mean zero random disturbance, and h_i and h_t are, respectively, the team‐specific and time‐specific fixed effects. For each ballpark, we sought to identify a ticket price at a level of seat quality that reflects the margin on which attendance changes. Since box seats and general admission seats generally exhibit relatively little variation in rate of sale, the marginal seat is apparently a reserved seat. For this reason, we defined our price variable, PRICE_i,t, to equal the log of the price of a seat at or near the middle range of reserved seating.16

The estimates, displayed in column 1 of table 5, reveal that all explanatory variables achieve statistical significance at the .10 level except lagged win proportion and capacity. Our four primary variables of interest, the new stadium variables, are all individually significant at the .10 level, with three of them significant at the .05 level. This result contrasts markedly to that of the revenue models, which found none of the stadium variables to attain individual significance. Apparently, the attendance data, unlike the revenue data, are sufficiently informative to yield inferences on the individual effects of stadium variables, notwithstanding the collinearity among them. In particular, the significant negative coefficients on the win‐interaction terms imply that new ballparks make attendance less elastic with respect to winning. The estimates indicate that a .010 rise in win proportion in an old ballpark causes attendance to rise by about 1.9%; this point estimate falls to virtually zero in the first year of a new ballpark and to about half its old value, or 0.9%, in subsequent seasons.17

Table 5 Fixed‐Effects Models of the Determinants of Attendance, Annual Observations, 1989–2001

Open New Window

Equation (9) implies functions for the first‐year and steady‐state effects analogous to (2) and (5). At a .500 win proportion, the first‐year effect is given by and the steady‐state effect takes the form For the estimates of these effects, refer to table 3, column 4. The estimate of the first‐year effect is highly significant and equal to .298.18 In contrast, the estimated steady‐state effect is rather small and statistically insignificant. Thus our estimated attendance effect, while significant, is only transitory. In fact, since the estimate of β₀ (.602) falls relatively far from one, the attendance effect is relatively short lived, and for the most part it subsides after just a few seasons. Obtaining two‐stage least‐squares estimates of the model in differenced form apparently leads to similar inferences, as shown in column 2 of table 5 and column 5 of table 3.

B. Revenue Predictions from Attendance Models

We depict the estimated attendance effect’s time pattern by simulating the effect for various horizons, as we did with our revenue estimates. But first we need to calibrate some parameters. To transform predicted attendance from logs to levels, we define the base level of attendance, ATT₋₁, to equal 2.07 million, the median 2001 attendance among the 16 teams playing in “old” ballparks. (By “old” we mean those ballparks not constructed during the recent 13‐year construction cycle.) Next, to translate attendance into dollars, we assume the marginal fan generates revenue equal to $17.80. This figure reflects typical prices faced by the marginal fan in 2001 at the 16 old ballparks. Again, we focus on prices at old ballparks in order to estimate a base price that is antecedent to any potential price shift induced by ballpark construction. The $17.80 figure equals the sum of $11.00 in ticket revenue and $6.80 in net revenue from parking and concessions. The ticket revenue represents the median value of PRICE_i,2001 for teams in old ballparks. The revenue from parking and concessions derives from Coffin’s (1996) estimate of $4.50 for Milwaukee in 1994. This figure we adjust to reflect the general level of 2001 ballpark prices by using the Fan Cost Index as compiled by Team Marketing Report (http://www.teammarketing.com). The median index at the 16 ballparks in 2001 represents a 51% increase over Milwaukee’s index for 1994; a proportionate increase in Coffin’s estimate yields our estimate of $6.80.

Now we can express the attendance effect in terms of its impact on revenue. Through M seasons the present value of the revenue increase attributable to additional attendance, ΔATT$PV_M, is given by Using (12) and letting the parameters β₀, β₁, …, and β₄ follow the stochastic process implied by the estimated fixed‐effects model, we simulate 5,000 realizations of ΔATT$PV_M for each of several horizons, M. The resulting mean values and confidence interval endpoints appear in table 6. Column 1 displays results from the levels model, and column 2 displays results from the differenced model.

Table 6 Present Value of Revenue Effect Implied by Attendance Models

Open New Window

The attendance results differ from the revenue results in two essential respects. First, the revenue effect from additional attendance, while substantial, accounts for only a fraction of the overall revenue effect. Specifically, the point estimates derived from the levels models imply that attendance accounts for $13 million out of $33 million, or 39%, of additional first‐season revenue and $32 million out of $133 million, or 24%, of additional revenue through five seasons. The declining percentage highlights the second difference, namely, that the attendance effect diminishes relatively quickly. The honeymoon does not last as long for attendance as it does for revenue. Clearly, then, additional ticket sales at current prices cannot account for the overall revenue effects of new ballparks.

To reconcile the predictions of the revenue and attendance models requires an increase in revenue per fan; in other words, the revenue effect must involve not just an increase in quantity but also an increase in price. Furthermore, relative to the attendance effect, the required price effect must exhibit greater time persistence. One such persistent effect, discussed in Section II, is the expansion of premium seating that is, club seats and luxury boxes. As Section II shows, however, a conservative estimate of additional revenue from premium seating yields $5 million per season, not nearly enough to account for the full amount of additional revenue. The remaining explanation must be that team management responds to the increased demand by raising ticket prices for standard seats, such as box, reserved, and general admission seats. Are such price increases supported by the data? If so, does their magnitude concur with the estimated revenue effects? We address these questions in the next subsection.

C. Evidence from Ticket Prices

We estimate the impact of stadium construction on ticket prices by considering the price of a field‐level box seat. Previously, we considered the price of a mid‐level reserved seat, which we took to represent the marginal seat because of its relatively variable rate of sale. Now our task is nearly the opposite, to estimate price changes for the broad range of seats that lie below the margin. In this regard, experience indicates that box seats routinely sell out at all prevailing prices, so increases in box prices represent pure increases in revenue not offset by lost sales.19

The data strongly indicate that ballpark construction results in higher ticket prices. Consider the 338 observations on field‐level box prices for nonexpansion teams from 1989–2001. For the 12 opening seasons in new ballparks, the log of price increased by an average of .247 over the previous season, while the mean annual increase for the other 326 observations was only .083. The difference of .164 implies that box prices jumped an additional 18% upon the opening of new ballparks. Moreover, estimating conditional means yields a similar result, as can be shown by applying a fixed‐effects model.

Let dBOXP_i,t denote the dependent variable, the first difference of the log of price. To capture the impact on demand from team performance, the explanatory variables include win proportion and lagged win proportion. The explanatory variables of interest are NEW_i,t, FIRST_i,t, and a lagged value, FIRST_i,t−1. These variables provide a reasonably flexible specification of the possible dynamic effects on price within our sample. The variable FIRST_i,t accounts for a price shift during the debut season, while the lagged value is intended to account for any reversion (or additional boost) during the second season. The variable NEW_i,t models a potential shift in the price variable’s trend growth rate. We obtain the following estimated model:20 where degrees of freedom = 295, partial , and Breusch‐Pagan .

Equation (13) implies a significant impact of new ballparks on ticket prices. The estimated coefficient of FIRST_i,t is .161, which differs significantly from zero at the .01 level. The other two stadium variables, however, have estimated coefficients that do not differ from zero individually or jointly; a test of the joint significance of the coefficients of FIRST_i,t−1 and NEW_i,t yields a chi‐square statistic of only 2.60 with two degrees of freedom. Thus the estimates detect no evidence of price reversion or shifts in the trend growth rate. This result concurs with a price effect that takes the form of a once‐and‐for‐all jump in price. A price jump of this form would account for the revenue effect exhibiting greater persistence than does the attendance effect.

Do the estimated price and revenue effects concur in magnitude? To facilitate comparison, assume that the price increase does occur once and for all. Proceeding on this assumption, we obtain a sharper estimate of the coefficient of FIRST_i,t by reestimating (13) with FIRST_i,t−1 and NEW_i,t omitted. This yields a slightly more conservative point estimate equal to .147, which implies a price jump of about 16%.

Experience indicates that, when teams increase ticket prices, they tend to increase them across all seating categories.21 Let us, therefore, take our 16% estimate for box seat prices as given and assume that it applies across the board to all sources of revenue. This assumption is merely heuristic and allows us to explore whether magnitudes of price increases can roughly account for estimated revenue effects. As discussed in Section II.D, we assume that base revenue in an old ballpark equals $100 million. Increasing this figure by 16% yields an additional $16 million per season. Adding $5 million from new premium seating implies a permanent revenue effect of $21 million per season (current values). Finally, add revenue from increased attendance, with the marginal fan assumed to generate 16% more than $17.80, or $20.65.

Table 6 reports the present value of the resulting revenue effect for various horizons. The values in columns 3 and 4 incorporate the predictions from the levels and differenced attendance models, respectively. Comparison with the revenue models’ predictions in table 4 reveals a remarkable similarity. The point estimates from the revenue model in levels, for example, were $33 million for the first season and $87 million through three seasons. As shown in column 3 of table 6, the price‐attendance models yield corresponding estimates higher by only $3 million, $36 million and $90 million. After five seasons, the revenue and price‐attendance models make nearly identical predictions, $133 million and $134 million, respectively. Even through 10 seasons, the predictions from the two methods differ by only $8 million, or less than 4%. Thus, the price and attendance models yield inferences that concur closely with those of the revenue models. This result lends additional support to our inference that new ballparks, for the most part, do pay for themselves.