production function, given their peculiar restrictions.
Our research provides some insight on the choice of models for estimating baseball
production functions. Keeping in mind the theoretical issues of causal relationships
between outputs, sharing of inputs, and correlation between disturbances, we conclude
that none of the more complicated estimation techniques is clearly superior to using
OLS to estimate the separate equations for winning percent and attendance. We
examined a causal model that is simultaneous only if disturbances
contemporaneously correlated and our empirical results do not support the
simultaneity. Regarding our canonical regression joint production model, both
theoretical and empirical considerations suggest the possibility of misleading
estimates. We used GLS to correct the OLS model of winning percent for the baseball
reality that average winning percent must always be 0.5. That correction requires the
omission of one observation for each league each season, but the estimates are
The existing baseball literature on production, winning percent, and attendance is
mostly comprised of single-equation models that use OLS estimation techniques.
Despite the theoretical and econometric problems that have often been raised in
discussions among those who do research on the economics of baseball, our empirical
results give these previous studies a relatively clean bill of health.
See Porter and
Scully ( 1982), Kahn ( 1982) and Ruggiero,
Gustafson ( 1995)
for examples of baseball production that use winning percent as the only output. Horowitz
( 1994) and Scully ( 1994) use the ratio wins to losses as the output measure.
Whether these two inputs capture all is debatable. In particular, slugging percent captures
the hitter's batting average and power, but potentially ignores their ability to drive in runs. Also,
team speed and fielding percent is ignored. The ratio of strikeouts to walks perhaps captures
pitcher's control, but does not necessarily measure the ability of pitchers to prevent runners from
scoring. Kahn ( 1993a) and Ruggiero,
Gustafson ( 1995) provide a more complete
list of inputs.
Horowitz ( 1994) invokes the so-called "Pythagoras Theorem" to evaluate the performance
of managers. The underlying basis for the analysis is a production relationship. Horowitz uses
the wins-losses ratio as output and the runs-opposition runs ratio as the input. In fact, both
variables are proxies for winning percent.
In the literature on baseball attendance, existing models include performance (winning
percent) as a determinant of attendance. In the context of these demand models, inclusion of
winning percent as an exogenous variable is appropriate. See Coffin ( 1996) for a further
discussion. In a production framework, both attendance and winning percent are endogenous
and are jointly produced.
It should be pointed out that the parameter estimates obtained in the solution of the
canonical regression are not unique. All parameters could be multiplied by a positive constant
without affecting the canonical correlation. The elasticity measures, however, are unique.