Table 8.

2SLS robustness of findings in Table 6 and Table 7 

VariablesModel 4Model 6Model 8Model 10
Panel A. Main variables
FirmCmplx10.049*** (0.000)0.038*** (0.000)
FirmCmplx20.340** (0.020)0.162** (0.029)
ExeFinKnow0.169** (0.024)1.402 (0.182)
AuditIndep0.012** (0.017)1.303** (0.035)
FirmCmplx1* ExeFinKnow−0.003** (0.045)
FirmCmplx1*AuditIndep0.0161 (0.593)
FirmCmplx2* ExeFinKnow−0.157 (0.312)
FirmCmplx2*AuditIndep0.189** (0.039)
Control variablesYesYesYesYes
Time fixed effectYesYesYesYes
Cluster (firm wise)YesYesYesYes
Panel B. Diagnostics
Endogenous regressors1212
Excluded instruments2424
Kleibergen–Paap rk LM5.60** (0.031)25.97*** (0.000)9.430*** (0.009)27.72*** (0.000)
Kleibergen–Paap rk wald F405.36356.43436.24419.16
Durbin–Wu–Hausman (DWH) test χ²0.916 (0.433)0.708 (0.402)
Anderson–Rubin Wald test F98.53*** (0.000)3.57*** (0.009)78.70*** (0.000)7.24*** (0.000)
Hansen J-statistics1.030, (0.310)0.960 (0.419)1.010 (0.315)1.059 (0.489)
Note(s):

Table 8 reports 2SLS robustness checks for Models 4, 6, 8 and 10. p -values are in parentheses. Standard errors are heteroskedasticity-robust and clustered at the firm level. Firm complexity is instrumented using its second and third lags (and, where applicable, lagged interaction instruments). The Kleibergen–Paap rk LM test evaluates underidentification (rejecting the null indicates the excluded instruments identify the endogenous regressors). The Kleibergen–Paap rk Wald F statistic assesses weak identification under cluster-robust conditions (large values indicate no weak-instrument concern relative to conventional thresholds). The Durbin–Wu–Hausman (DWH) test examines whether the potentially endogenous regressor(s) can be treated as exogenous; where the test is not reported, ivreg2 indicates collinearity/identification issues in the restricted equation. Because the DWH tests fail to reject exogeneity where available, the 2SLS results are interpreted as conservative robustness checks rather than evidence that the baseline estimates are inconsistent. The Anderson–Rubin Wald test provides weak-instrument-robust inference on the joint significance of the endogenous regressor(s). The Hansen J test (reported for overidentified models) evaluates overidentifying restrictions; failure to reject (e.g. p > 0.10) provides no evidence against instrument exogeneity. *p < 0.10, **p < 0.05, ***p < 0.01

Source(s): Authors’ own work

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