Table 3. GMM Estimates for the...

Table 3.

GMM Estimates for the Coefficient of Relative Risk Aversion: Linearized Model.

	Short Sample (1960–2014)					Full Sample (1928γ2014)
	T = 55 and N = 1					T = 87 and N = 1
	Reported Dec.	Garbage Dec.	P-J Dec.	Q4-Q4 Dec.	Unfiltered T.A.	Reported Dec.	Unfiltered T.A.
γ	1,465.83	20.16	79.16	81.45	29.38	149.35	14.98
se(γ)	10,010.85	13.09	89.35	59.62	20.36	192.99	8.38
Btrp c.i._95%	(−350.3,2,784,373.2)	(3.6,81.2)	(−103.6,1,687,182.3)	(12.7,958.1)	(4.6,142.3)	(−415.5,2,032,094.4)	(4.4,47.8)
GMM-AR c.i.₉₅o∕₀	unb./disjointed	(4.4, 115.9)	unb./disjointed	(18.3, 4359.1)	(4.9, 201.6)	unb./disjointed	(4.4, 66.0)
J_T	0.00	0.00	0.00	0.00	0.00	0.00	0.00
p(rank)	0.88	0.01	0.28	0.04	0.01	0.38	0.01
p(corr)	0.90	0.00	0.32	0.03	0.00	0.30	0.00

	Short Sample (1960–2014)					Full Sample (1928γ2014)
	T = 55 and N = 1					T = 87 and N = 1
	Reported Dec.	Garbage Dec.	P-J Dec.	Q4-Q4 Dec.	Unfiltered T.A.	Reported Dec.	Unfiltered T.A.
γ	1,465.83	20.16	79.16	81.45	29.38	149.35	14.98
se(γ)	10,010.85	13.09	89.35	59.62	20.36	192.99	8.38
Btrp c.i._95%	(−350.3,2,784,373.2)	(3.6,81.2)	(−103.6,1,687,182.3)	(12.7,958.1)	(4.6,142.3)	(−415.5,2,032,094.4)	(4.4,47.8)
GMM-AR c.i.₉₅o∕₀	unb./disjointed	(4.4, 115.9)	unb./disjointed	(18.3, 4359.1)	(4.9, 201.6)	unb./disjointed	(4.4, 66.0)
J_T	0.00	0.00	0.00	0.00	0.00	0.00	0.00
p(rank)	0.88	0.01	0.28	0.04	0.01	0.38	0.01
p(corr)	0.90	0.00	0.32	0.03	0.00	0.30	0.00

Description: This table shows estimates of the coefficient of relative risk aversion (γ) using the linear GMM moment condition:

E (R_{t}^{e}) - γ \times C o v (R_{t}^{e}, △ C_{t + 1}) = 0.

The market excess return is the single test asset. Below the GMM estimate of γ is the GMM standard error, and the 95% confidence interval of γ according to a pairwise bootstrap or the GMM-AR test. J_T is the value of the objective function, p(rαnk), is the p-value for the GMM-rank test which is equivalent to test the hypothesis HO: $C o v (R_{t}^{e}, △ C_{t + 1}) = 0. p (c o r r)$ ⁠, is the p-value for a direct test of the correlation coefficient.

Interpretation: A linearized version of the model is robust to the “GMM trap” problem. Now both the bootstrap and GMM-AR confidence intervals allow for the same conclusion that garbage, Q4-Q4 and unfiltered consumption help to explain the equity premium. GMM standard errors require testing at a higher significance level to come to the same conclusion.

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