Table 7 IV tests of CMEP and health.

From: A chronic multidimensional measure of energy poverty and its impacts on physical and mental health

 

(1)

(2)

(3)

(4)

(5)

(6)

 

Physical

Mental

Physical

Mental

Physical

Mental

 

Lewbel internal IV

Lewbel internal & external IV

CMEP

−0.8704***

1.2340**

−0.4166***

1.2700***

−0.2980***

1.2266***

 

(0.2247)

(0.5405)

(0.1254)

(0.3183)

(0.0422)

(0.1462)

Control

Yes

Yes

Yes

Yes

Yes

Yes

Provincial FE

Yes

Yes

Yes

Yes

Yes

Yes

Num. obs.

10,499

10,453

10,499

10,453

10,499

10,453

First stage

 

F-statistic test

23.61

43.49

1696.93

527.25

1.2e + 06

2.6e + 05

Pagan–Hall test

138.076

112.146

141.296

116.187

179.745

140.643

Bresuch–Pagan test

152.106

113.784

142.398

116.705

180.158

141.120

  1. Robust standard errors, clustered at the individual level, are reported in parentheses. The first-stage F-statistic in IV estimation assesses instrument strength, as weak instruments—those weakly correlated with the endogenous variable—can lead to biased estimates. According to Staiger and Stock (1997), an F-statistic above 10 generally rules out weak instruments. The Pagan–Hall test examines heteroscedasticity in the error term, which is crucial for Lewbel’s (2012) heteroscedasticity-based IV method; a significant result justifies using internally generated IVs. The Breusch–Pagan test similarly detects heteroscedasticity, indicating whether error variance is constant. In IV models, significant heteroscedasticity supports the use of robust standard errors or alternative approaches such as Lewbel’s method.
  2. ***p < 0.01, **p < 0.05.
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