Table 2. Open in new tab Test of...

Dependent variable	Model	All variables	VAR-E variables	Macro variables	Individual macro variables (⁠ $Δ c_{t}, Δ w_{t}, Δ h p_{t}, Δ f t s e_{t}$ ⁠, respectively)
Expectational errors
$y_{t} -_{t - 1} y_{t}^{e}$	Balance	0.001***	0.009***	0.297	0.479, 0.089*, 0.284, 0.599
	Rolling	0.002***	0.018**	0.194	0.255, 0.169, 0.136, 0.837
	Meta	0.001***	0.002***	0.298	0.438, 0.108, 0.348, 0.592
Equation residuals
Actual Output residuals	WHOL	–	–	0.298	0.438, 0.108, 0.348, 0.592
ROLL	–	–	0.330	0.743, 0.072, 0.362, 0.914
META	–	–	0.360	0.868, 0.089, 0.323, 0.472
Expected Output residuals	WHOL	–	–	0.039**	0.041**, 0.631, 0.616, 0.061
ROLL	–	–	0.055*	0.226, 0.348, 0.458, 0.101
META	–	–	0.086*	0.275, 0.573, 0.422, 0.094*
Output Uncertainty residuals	WHOL	–	–	0.529	0.771, 0.400, 0.201, 0.657
ROLL	–	–	0.130	0.603, 0.470, 0.888, 0.024
META	–	–	0.052	0.170, 0.460, 0.863, 0.007

Dependent variable	Model	All variables	VAR-E variables	Macro variables	Individual macro variables (⁠ $Δ c_{t}, Δ w_{t}, Δ h p_{t}, Δ f t s e_{t}$ ⁠, respectively)
Expectational errors
$y_{t} -_{t - 1} y_{t}^{e}$	Balance	0.001***	0.009***	0.297	0.479, 0.089*, 0.284, 0.599
	Rolling	0.002***	0.018**	0.194	0.255, 0.169, 0.136, 0.837
	Meta	0.001***	0.002***	0.298	0.438, 0.108, 0.348, 0.592
Equation residuals
Actual Output residuals	WHOL	–	–	0.298	0.438, 0.108, 0.348, 0.592
ROLL	–	–	0.330	0.743, 0.072, 0.362, 0.914
META	–	–	0.360	0.868, 0.089, 0.323, 0.472
Expected Output residuals	WHOL	–	–	0.039**	0.041**, 0.631, 0.616, 0.061
ROLL	–	–	0.055*	0.226, 0.348, 0.458, 0.101
META	–	–	0.086*	0.275, 0.573, 0.422, 0.094*
Output Uncertainty residuals	WHOL	–	–	0.529	0.771, 0.400, 0.201, 0.657
ROLL	–	–	0.130	0.603, 0.470, 0.888, 0.024
META	–	–	0.052	0.170, 0.460, 0.863, 0.007

Table 2.

Test of exclusion restrictions

Dependent variable	Model	All variables	VAR-E variables	Macro variables	Individual macro variables (⁠ $Δ c_{t}, Δ w_{t}, Δ h p_{t}, Δ f t s e_{t}$ ⁠, respectively)
Expectational errors
$y_{t} -_{t - 1} y_{t}^{e}$	Balance	0.001***	0.009***	0.297	0.479, 0.089*, 0.284, 0.599
	Rolling	0.002***	0.018**	0.194	0.255, 0.169, 0.136, 0.837
	Meta	0.001***	0.002***	0.298	0.438, 0.108, 0.348, 0.592
Equation residuals
Actual Output residuals	WHOL	–	–	0.298	0.438, 0.108, 0.348, 0.592
	ROLL	–	–	0.330	0.743, 0.072, 0.362, 0.914
	META	–	–	0.360	0.868, 0.089, 0.323, 0.472
Expected Output residuals	WHOL	–	–	0.039**	0.041**, 0.631, 0.616, 0.061
	ROLL	–	–	0.055*	0.226, 0.348, 0.458, 0.101
	META	–	–	0.086*	0.275, 0.573, 0.422, 0.094*
Output Uncertainty residuals	WHOL	–	–	0.529	0.771, 0.400, 0.201, 0.657
	ROLL	–	–	0.130	0.603, 0.470, 0.888, 0.024
	META	–	–	0.052	0.170, 0.460, 0.863, 0.007

Dependent variable	Model	All variables	VAR-E variables	Macro variables	Individual macro variables (⁠ $Δ c_{t}, Δ w_{t}, Δ h p_{t}, Δ f t s e_{t}$ ⁠, respectively)
Expectational errors
$y_{t} -_{t - 1} y_{t}^{e}$	Balance	0.001***	0.009***	0.297	0.479, 0.089*, 0.284, 0.599
	Rolling	0.002***	0.018**	0.194	0.255, 0.169, 0.136, 0.837
	Meta	0.001***	0.002***	0.298	0.438, 0.108, 0.348, 0.592
Equation residuals
Actual Output residuals	WHOL	–	–	0.298	0.438, 0.108, 0.348, 0.592
	ROLL	–	–	0.330	0.743, 0.072, 0.362, 0.914
	META	–	–	0.360	0.868, 0.089, 0.323, 0.472
Expected Output residuals	WHOL	–	–	0.039**	0.041**, 0.631, 0.616, 0.061
	ROLL	–	–	0.055*	0.226, 0.348, 0.458, 0.101
	META	–	–	0.086*	0.275, 0.573, 0.422, 0.094*
Output Uncertainty residuals	WHOL	–	–	0.529	0.771, 0.400, 0.201, 0.657
	ROLL	–	–	0.130	0.603, 0.470, 0.888, 0.024
	META	–	–	0.052	0.170, 0.460, 0.863, 0.007

Notes. Statistics refer to the p-values of the F-tests of the various null hypotheses based on the various models described in the text. Superscripts *, **, and *** highlight significance at the 10%, 5%, and 1% levels of significance, respectively.

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