Table 2.

Marginal Effects of Probit and IV‐Probit Estimates

(a) Probit Estimation
	(1)	(2)	(3)	(4)	(5)
ln case volume	−0.0086***	−0.0104***	−0.0115***	−0.0142***	−0.0123***
	(0.0015)	(0.0015)	(0.0020)	(0.0021)	(0.0022)
Patient characteristics	No	Yes	No	Yes	Yes
Hospital charcteristics	No	No	Yes	Yes	Yes
Socioeconomic indicators	No	No	No	No	Yes
Settlement structure indicators	No	No	No	No	Yes
Observations	89,541	89,541	89,541	89,541	89,541
Number of hospitals	1,262	1,262	1,262	1,262	1,262

(b) IV‐Probit; Instrument: Number of Potential Patients and Further Hospitals in the Regional Area
	(6)	(7)	(8)	(9)	(10)
Ln case volume	−0.0191***	−0.0247***	−0.0289***	−0.0355***	−0.0334***
	(0.0037)	(0.0039)	(0.0055)	(0.0058)	(0.0061)
Patient characteristics	No	Yes	No	Yes	Yes
Hospital charcteristics	No	No	Yes	Yes	Yes
Socioeconomic indicators	No	No	No	No	Yes
Settlement structure indicators	No	No	No	No	Yes
First‐stage F‐statistic	78.1848	80.0255	47.8049	48.2419	42.3054
Test for endogeneity (p‐value)	0.0005	0.0000	0.0002	0.0000	0.0001
Overidentification test (p‐value)	0.0043	0.0006	0.0936	0.039	0.0999
Observations	89,541	89,541	89,541	89,541	89,541
Number of hospitals	1,262	1,262	1,262	1,262	1,262

(c) IV‐Probit; Instrument: Number of Potential Patients per Hospital in the Regional Area
	(11)	(12)	(13)	(14)	(15)
Ln case volume	−0.0138***	−0.0176***	−0.0217***	−0.0280***	−0.0259***
	(0.0037)	(0.0041)	(0.0060)	(0.0066)	(0.0071)
Patient characteristics	No	Yes	No	Yes	Yes
Hospital charcteristics	No	No	Yes	Yes	Yes
Socioeconomic indicators	No	No	No	No	Yes
Settlement structure indicators	No	No	No	No	Yes
First‐stage F‐statistic	186.7512	189.1469	130.9806	130.7457	119.6255
Test for endogeneity (p‐value)	0.0930	0.0372	0.0557	0.0175	0.0299
Observations	89,541	89,541	89,541	89,541	89,541
Number of hospitals	1,262	1,262	1,262	1,262	1,262

Clustered standard errors (at the hospital level) in parentheses. *p < .10, **p < .05, ***p < .01.