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Table 8 Instrumental-variables regression for panel data (Baltagi–Chang estimator)

From: Interferon-alpha 2 but not Interferon-gamma serum levels are associated with intramuscular fat in obese patients with nonalcoholic fatty liver disease

xtivreg IMTG HS at US (HS at US = VAT), re nosa (robust)

G2SLS random-effects IV regression

Number of obs = 80

Group variable: WC

Number of groups = 64

R-sq

Obs per group

Within = 0.1970

Min = 1

Between = 0.03012

Avg = 2

Overall = 0.1028

Max = 6

Wald χ2 (1) = 11.09

Corr (u_i, X) = 0 (assumed)

Prob > χ2 = 0.0009

d. v.: IMTG

Coef.

Rob. Std. err.

z

P > |z|

[95% Conf. interval]

i.v.

 HS at US

0.5199847

0.156167

3.33

0.001

0.2139031 to − 0.8260663

 HS at US

0 (omitted)

    

 _cons

1.719254

0.270595

6.35.

0.000

1.188903 to 0.249616

 Sigma_u

0.48060539

    

 Sigma_e

0.74235381

    

 rho

0.2953461 (fraction of variance due to u_i)

{p 0 16 − 12}Instrumented: HS at US{p_end}

{p 0 16 − 12}Instruments: HS at US VAT{p_end}

  1. The instrument (VAT) cannot be correlated with the dependent (IMTG) in the explanatory equation. In other words, the instrument cannot suffer from the same problem as the original predicting variable (IMTG predicted by HS at US). If this condition is met, then the instrument is said to satisfy the exclusion restriction. As grouping variable was chosen an index of visceral adiposity, i.e., WC
  2. IMTG intramusclolar triglycerides, HS at US hepatic steatosis at Ultrasonography, VAT visceral adipose tissue, d.v. dependent variable, i.v. independent variable