Table 1.

Results of the stochastic frontier model fit to the longitudinal panel dataset (1984–2017)

Variable	Coef.†	SE‡	Avg. marginal effect, $§
Base cost inefficiency model
ln Attendance (visitor-hours)/acre	0.255***	0.014	26.16
ln Capital expenditures/acre‡	0.027***	0.004	6.08
ln Revenue/acre‡	0.064***	0.007	7.78
ln Labor (person-hours)/acre§	0.422***	0.015	10.12
Constant	3.087***	0.062
Uσ constant	−3.407***	0.092
Vσ constant	−3.479***	0.059
θ constant	0.329***	0.020
σU	0.182***	0.008
σV	0.176***	0.005
λ	1.037***	0.012
Base cost inefficiency model with state-specific climate covariates
ln Attendance (visitor-hours)/acre	0.250***	0.015	25.43
ln Capital expenditures/acre‡	0.027***	0.004	6.07
ln Revenue/acre‡	0.064***	0.008	7.76
ln Labor (person-hours)/acre§	0.425***	0.016	10.20
Precipitation, cm/y	2.5e−4	3.6e−4	93.73
Average temperature, °C	0.003*	1.7e−3	11.51
Constant	3.097***	0.069
Uσ constant	−3.401***	0.092
Vσ constant	−3.485***	0.059
θ constant	0.319***	0.023
σU	0.183***	0.008
σV	0.175***	0.005
λ	1.043***	0.012

^*P < 0.05, ***P < 0.001; n = 1,700 (50 states × 34 y); number of pseudorandom draws used in each model = 250.

^†All estimated coefficients can be interpreted as point elasticities, meaning they indicate the percentage change in ln Operating Expenditures given a 1% increase (decrease) in that coefficient’s respective variable.

^‡Confidence intervals are provided in SI Appendix, Table S1.

^§Average marginal effects are the monetary change in operating expenditures corresponding to a 1% increase (decrease) in each variable; they are calculated as ${\overline{\mathit{x}}}^{\mathit{\beta }}\times \mathbf{l}\mathbf{n}\left(\overline{\mathit{x}}\right)$, where $\overline{\mathit{x}}$ is the variable mean.