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Table 6 Results of Bewley transformation from instrument variable estimation

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

\(LnZ1\)

Coefficient

p value

\(\Delta LnZ_{1}\)

− 0.295

0.167

\(LnVIX\)

0.156

0.000

\(WEI\)

0.002

0.612

Cons

22.899

0.000

Number of obs = 55

F(3, 51) = 7.89

Prob > F = 0.0002

Total (centered) SS = 0.3189746795

Total (uncentered) SS = 30,134.53036

Residual SS = 0.3008455664

Centered R2 = 0.0568

Uncentered R2 = 1.0000

Root MSE = 0.07396

Under identification test (Anderson canon. corr. LM statistic): 22.065

Chi-sq(1) p value = 0.0000

Weak identification test (Cragg-Donald Wald F statistic): 34.168

Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38

15% maximal IV size 8.96

20% maximal IV size 6.66

25% maximal IV size 5.53

Sargan statistic (overidentification test of all instruments): 0.000

(Equation exactly identified)