Moment Conditions Selection Based on Adaptive Penalized Empirical Likelihood

Table 3

EL and GMM shrinkage estimators of the moment selection coefficients¹.

Method	IV	edu	edu^2	edu_𝑓	Age	edu ∗ age	𝜔^∗𝑖,𝑡	𝜔𝑖,𝑡
	𝛽0	𝛽1,0	𝛽2,0	𝛽3,0	𝛽4,0	𝛽5,0	𝛽6,0	𝛽7,0
ada-EL	EL^2	−0.0016	−0.0145	−0.0022	0.0049	−0.0123	−0.0008	−0.0441
		(0.0071)	(0.0518)	(0.0057)	(0.1145)	(0.4698)	(0.0074)	(0.0996)
		0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	−0.0306
	SEL^2,4	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0097)
	EL^3	−0.0030	0.0251	−0.0023	0.0357	0.0385	−0.0015	0.0496
		(0.0094)	(0.0553)	(0.0065)	(0.2165)	(0.6342)	(0.0091)	(0.1143)
		0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	−0.0273
	SEL^3,5	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0081)
ada-GMM	GMM^2	−0.0019	−0.0145	−0.0021	0.0048	−0.0123	−0.0007	−0.0442
		(0.0073)	(0.0518)	(0.0057)	(0.1145)	(0.4696)	(0.0071)	(0.0995)
		0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	−0.0306
	SGMM^2,4	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0097)
	GMM^3	−0.0034	0.0253	−0.0025	0.0357	0.0382	−0.0018	0.0496
		(0.0095)	(0.0558)	(0.0063)	(0.2166)	(0.6348)	(0.0094)	(0.1142)
		0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	−0.0273
	SGMM^3,5	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0076)

For detailed instructions see Remark 3.