Table 1. The Equity Premium and...

Table 1.

The Equity Premium and Alternative Consumption Measures.

	Short Sample (1960-2014)					Full Sample (1928-2014)
	$E [R_{m}^{e}] = 5.8$					$E [R_{m}^{e}] = 7.3$
	Reported Dec.	Garbage Dec.	P-J Dec.	Q4-Q4 Dec.	Unfiltered T.A.	Reported Dec.	Unfiltered T.A.
Panel A: Identification
Covariance	0.39	26.04	7.29	7.09	19.64	4.87	48.54
Btrp c.i._95%	(−6.8,8.2)	(11.2,45.2)	(−7.6,24.8)	(−0.4,15.8)	(6.2,35.8)	(−7.0,17.4)	(24.5,79.4)
Correlation	0.02	0.58	0.14	0.29	0.45	0.11	0.60
Btrp c.i._95%	(−0.3,0.3)	(0.3,0.7)	(−0.2,0.4)	(−0.0,0.5)	(0.2,0.6)	(−0.2,0.4)	(0.4,0.7)
Beta	0.23	3.21	0.72	3.32	2.95	1.03	3.00
Btrp c.i._95%	(−3.2,3.6)	(1.9,4.5)	(−0.7,2.1)	(0.4,6.2)	(1.4,4.5)	(−0.9,2.9)	(2.2,3.9)
Panel B: Implied Economic Quantities
Rel. Risk Aversion, γ	1,465.83	20.16	79.16	81.45	29.38	149.35	14.98
Btrp c.i.₉₅„_%	(−2,598.8,2,365.5)	(1.8,70.2)	(−993.5,920.1)	(−424.2,807.7)	(4.6,123.2)	(−1,650.4,1,570.2)	(4.8,38.3)
Price of Risk, λ_%	25.07	1.63	8.07	1.74	1.96	7.07	2.42
Btrp c.i.₉₅„_%	(−37.3,45.5)	(0.2,4.1)	(−89.7,99.0)	(−6.0,16.2)	(0.3,6.2)	(−71.3,63.8)	(1.0,4.4)
Equity Premium, %	0.04	2.60	0.73	0.71	1.96	0.49	4.85
Btrp c.i._95%	(−0.7,0.8)	(1.1,4.6)	(−0.7,2.4)	(−0.0,1.6)	(0.6,3.6)	(−0.7,1.7)	(2.4,8.0)

	Short Sample (1960-2014)					Full Sample (1928-2014)
	$E [R_{m}^{e}] = 5.8$					$E [R_{m}^{e}] = 7.3$
	Reported Dec.	Garbage Dec.	P-J Dec.	Q4-Q4 Dec.	Unfiltered T.A.	Reported Dec.	Unfiltered T.A.
Panel A: Identification
Covariance	0.39	26.04	7.29	7.09	19.64	4.87	48.54
Btrp c.i._95%	(−6.8,8.2)	(11.2,45.2)	(−7.6,24.8)	(−0.4,15.8)	(6.2,35.8)	(−7.0,17.4)	(24.5,79.4)
Correlation	0.02	0.58	0.14	0.29	0.45	0.11	0.60
Btrp c.i._95%	(−0.3,0.3)	(0.3,0.7)	(−0.2,0.4)	(−0.0,0.5)	(0.2,0.6)	(−0.2,0.4)	(0.4,0.7)
Beta	0.23	3.21	0.72	3.32	2.95	1.03	3.00
Btrp c.i._95%	(−3.2,3.6)	(1.9,4.5)	(−0.7,2.1)	(0.4,6.2)	(1.4,4.5)	(−0.9,2.9)	(2.2,3.9)
Panel B: Implied Economic Quantities
Rel. Risk Aversion, γ	1,465.83	20.16	79.16	81.45	29.38	149.35	14.98
Btrp c.i.₉₅„_%	(−2,598.8,2,365.5)	(1.8,70.2)	(−993.5,920.1)	(−424.2,807.7)	(4.6,123.2)	(−1,650.4,1,570.2)	(4.8,38.3)
Price of Risk, λ_%	25.07	1.63	8.07	1.74	1.96	7.07	2.42
Btrp c.i.₉₅„_%	(−37.3,45.5)	(0.2,4.1)	(−89.7,99.0)	(−6.0,16.2)	(0.3,6.2)	(−71.3,63.8)	(1.0,4.4)
Equity Premium, %	0.04	2.60	0.73	0.71	1.96	0.49	4.85
Btrp c.i._95%	(−0.7,0.8)	(1.1,4.6)	(−0.7,2.4)	(−0.0,1.6)	(0.6,3.6)	(−0.7,1.7)	(2.4,8.0)

Description: Panel A reports the covariance, correlation and beta of alternative consumption measures with the market excess return (T = 55, N = 1). Panel B shows the implied coefficient of relative risk aversion (γ) exploiting the linearized relationship $E [R_{m}^{e}] = γ \times Cov (R_{m, t}^{e}, Δ C_{t}) .$ ⁠. The price of risk is defined as λ = γ ∕Var(ΔC_t). The implied equity premium imposes γ = 10, the maximum level of risk aversion considered plausible by Mehra and Prescott (1985). The dataset is the same as in Kroencke (2017) and Kleibergen and Zhan (2020); equity returns below Dec. (TA.) are measured at the end of December (Time-Aggregated). Bootstrap re-samples are used to determine 95% confidence intervals.

Interpretation: Reported consumption is insignificantly correlated with the market excess return (and might be regarded as a “useless” factor) and does not explain the equity premium; also known as the equity premium puzzle (Mehra and Prescott, 1985). Alternative consumption measures like garbage or unfiltered consumption have large and significant correlation coefficients and explain a part but not all of the equity premium. Estimated parameters (γ and λ) are later used to benchmark with other methods.

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