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Table 5 Results from first stage regressions of Bewley transformation

From: Did weekly economic index and volatility index impact US food sales during the first year of the pandemic?

\(\Delta LnZ_{1t - 1}\)

Coefficient

p value

\(LnZ_{1t - 1}\)

− 0.772

0.000

\(LnVIX\)

0.120

0.000

\(WEI\)

0.001

0.617

Cons

17.682

0.000

Sanderson-Windmeijer multivariate F test of excluded instruments: F (1, 51) = 34.17,

Prob > F = 0.0000

Under identification Test: Anderson canon. corr. LM statistic:

Chi-sq(1) = 22.07, p value = 0.0000

Weak identification Test: Cragg-Donald Wald F statistic

34.17***

Weak-instrument-robust inference

Anderson-Rubin Wald test F(1,51) = 2.97 p value = 0.0907

Anderson-Rubin Wald test Chi-sq(1) = 3.21 p value  = 0.0733

Stock-Wright LM S statistic Chi-sq(1) = 3.03 p value  = 0.0817

Number of observations N = 55

Number of regressors K = 4

Number of endogenous regressors K1 = 1

Number of instruments L = 4

Number of excluded instruments L1 = 1

  1. Notes: *** indicate significant at 1% level of significance