Table 4.

Error Components Models for Log Real Annual Earnings (no calendar time effects)

	RE + AR (1)	RE + ARMA (1, 1)	Random-Walk RE + ARMA (1, 1)	Random-Growth RE + ARMA (1, 1)
	(I)	(II)	(III)	(IV)
${\mathrm{\sigma }}_{\mathrm{\mu }}^2$	.114 (.008)	.070 (.012)	.090 (.015)	.092 (.005)
ρ	.354 (.017)	.906 (.026)	.622 (.025)	.657 (.069)
${\mathrm{\sigma }}_{\mathrm{\eta }}^2$	.167 (.013)	-	-	-
θ	-	−.670 (.017)	−.344 (.045)	−.362 (.092)
${\mathrm{\sigma }}_{\mathrm{\xi }}^2$	-	.188 (.013)	.169 (.016)	.166 (.007)
${\mathrm{\sigma }}_{\mathrm{\omega }}^2$	-	-	.159a (.025)	-
${\mathrm{\sigma }}_{\mathrm{\varphi }}^2$	-	-	-	.462a (.069)
Chi-squared (df)	2388 (550)	2262 (549)	2094 (548)	2080 (548)

Notes: Standard errors in parentheses

All coefficients significant at 10 percent level

RE=random effect

^aParameter multiplied by 100

Model I:	(1) εia = μi + νia
	(2) νia = ρνi, a−1 + ηia
Model II:	(1), (2), plus
	(3) ηia = ξia + θξi, a−1
Model III:	(2), (3), plus
	(1′) εia = μia + νia
	(4) μia = μi, a−1 + ωia
	with ${\mathrm{\sigma }}_{\mathrm{\mu }}^2=\text{Var}({\mathrm{\mu }}_{\mathrm{i}1})$
Model IV:	(2), (3), plus
	(1″) εia = μi + aϕi + νia

All primary error components assumed independent.