Table 6. Open in new tab Negative...

(1)

(2)

(3)

(4)

β_{1} = β_{2}

Avg. performance (season)

−0.0778***

−0.0531**

−0.0523**

−0.0528**

(0.0230)

(0.0228)

(0.0227)

DFB cup referee (d)

0.0478

0.0561

0.0554

0.0556

(0.1653)

(0.1664)

(0.1676)

(0.1684)

International referee (d)

0.1692

0.1752

0.1746

0.1727

(0.1163)

(0.1166)

(0.1169)

(0.1162)

Age

0.0004

0.0001

0.0009

(0.0268)

(0.0266)

(0.0270)

(0.0267)

Tenure (BL)

−0.0874***

−0.0885***

−0.0895***

(0.0297)

(0.0292)

(0.0295)

(0.0292)

Expected pause

0.6356***

0.6155***

0.6167***

0.6185***

(0.1479)

(0.1483)

(0.1474)

(0.1472)

Type II errors

0.0640

} p = 0.3422

(0.0405)

Type I errors

0.0986***

(0.0317)

Type II errors (ATT ahead)

0.0266

} p = 0.3120

(0.0502)

Type II errors (ATT behind)

0.0998*

(0.0577)

Type I errors (ATT ahead)

0.1229***

} p = 0.3163

(0.0418)

Type I errors (ATT behind)

0.0744**

(0.0361)

Type II errors (members ahead)

0.0207

} p = 0.2636

(0.0546)

Type II errors (members behind)

0.1025*

(0.0553)

Type I errors (members ahead)

0.1326***

} p = 0.1605

(0.0391)

Type I errors (members behind)

0.0610

(0.0404)

Referee FE

Yes

3704

Table 6.

Open in new tab

Negative Binomial Models on Pause between Games

	(1)	(2)	(3)	(4)	$β_{1} = β_{2}$
Avg. performance (season)	−0.0778***	−0.0531**	−0.0523**	−0.0528**
	(0.0230)	(0.0228)	(0.0227)	(0.0227)
DFB cup referee (d)	0.0478	0.0561	0.0554	0.0556
	(0.1653)	(0.1664)	(0.1676)	(0.1684)
International referee (d)	0.1692	0.1752	0.1746	0.1727
	(0.1163)	(0.1166)	(0.1169)	(0.1162)
Age	0.0004	0.0004	0.0001	0.0009
	(0.0268)	(0.0266)	(0.0270)	(0.0267)
Tenure (BL)	−0.0874***	−0.0885***	−0.0885***	−0.0895***
	(0.0297)	(0.0292)	(0.0295)	(0.0292)
Expected pause	0.6356***	0.6155***	0.6167***	0.6185***
	(0.1479)	(0.1483)	(0.1474)	(0.1472)
Type II errors		0.0640			} p = 0.3422
		(0.0405)
Type I errors		0.0986***
		(0.0317)
Type II errors (ATT ahead)			0.0266		} p = 0.3120
			(0.0502)
Type II errors (ATT behind)			0.0998*
			(0.0577)
Type I errors (ATT ahead)			0.1229***		} p = 0.3163
			(0.0418)
Type I errors (ATT behind)			0.0744**
			(0.0361)
Type II errors (members ahead)				0.0207	} p = 0.2636
				(0.0546)
Type II errors (members behind)				0.1025*
				(0.0553)
Type I errors (members ahead)				0.1326***	} p = 0.1605
				(0.0391)
Type I errors (members behind)				0.0610
				(0.0404)
Referee FE	Yes	Yes	Yes	Yes
N	3704	3704	3704	3704

	(1)	(2)	(3)	(4)	$β_{1} = β_{2}$
Avg. performance (season)	−0.0778***	−0.0531**	−0.0523**	−0.0528**
	(0.0230)	(0.0228)	(0.0227)	(0.0227)
DFB cup referee (d)	0.0478	0.0561	0.0554	0.0556
	(0.1653)	(0.1664)	(0.1676)	(0.1684)
International referee (d)	0.1692	0.1752	0.1746	0.1727
	(0.1163)	(0.1166)	(0.1169)	(0.1162)
Age	0.0004	0.0004	0.0001	0.0009
	(0.0268)	(0.0266)	(0.0270)	(0.0267)
Tenure (BL)	−0.0874***	−0.0885***	−0.0885***	−0.0895***
	(0.0297)	(0.0292)	(0.0295)	(0.0292)
Expected pause	0.6356***	0.6155***	0.6167***	0.6185***
	(0.1479)	(0.1483)	(0.1474)	(0.1472)
Type II errors		0.0640			} p = 0.3422
		(0.0405)
Type I errors		0.0986***
		(0.0317)
Type II errors (ATT ahead)			0.0266		} p = 0.3120
			(0.0502)
Type II errors (ATT behind)			0.0998*
			(0.0577)
Type I errors (ATT ahead)			0.1229***		} p = 0.3163
			(0.0418)
Type I errors (ATT behind)			0.0744**
			(0.0361)
Type II errors (members ahead)				0.0207	} p = 0.2636
				(0.0546)
Type II errors (members behind)				0.1025*
				(0.0553)
Type I errors (members ahead)				0.1326***	} p = 0.1605
				(0.0391)
Type I errors (members behind)				0.0610
				(0.0404)
Referee FE	Yes	Yes	Yes	Yes
N	3704	3704	3704	3704

Notes: Negative binomial estimates. Average marginal effects; (d) for discrete change of dummy variable from 0 to 1. The discrete dependent variable measures the number of game days between the present game and the next one in which the referee is used (0 when referee is immediately used in the next game). The control variables measure performance in the game—in standard deviations and with mean 0, whether a referee was also refereeing in the DFB Cup or internationally (Champions League or Euro League) in this season, the age at the time of the game as well as tenure in the Bundesliga. We furthermore calculate the “expected pause” based on the number of referees in the referee pool in a given season and the number of available games and match days. The last column presents the p-value for test of equality for the indicated coefficients. Standard errors in parentheses are clustered at the referee level.

***

p < 0.01,

p < 0.05,

p < 0.1.

This Feature Is Available To Subscribers Only