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Table 6 Marginal effect (mean derivative, \(\hat{D}_{k}\)) estimates and significance testing results. Linear versus optimal cross-validated ANN results

From: Tax avoidance and earnings management: a neural network approach for the largest European economies

Variable

GAAP_ETR

CASH_ETR

BTD

Linear

ANN (\(m = 2\))

Linear

ANN \((m = 1\))

Linear

ANN (\(m = 1\))

ACCRUALS

0.0008**

(0.0005)

0.0066***

(0.0321)

0.0005

(0.0006)

0.0043***

(0.0209)

0.0002

(0.0003)

0.0008

(0.0080)

SIZE

−0.0057***

(0.0007)

−0.0050***

(0.0361)

0.0021**

(0.0010)

0.0032

(0.0124)

−0.0009***

(0.0002)

−0.0006***

(0.0012)

LEV

0.0725***

(0.0075)

0.0850***

(0.0324)

0.0097

(0.0086)

0.0093***

(0.0246)

0.0117***

(0.0036)

0.0105***

(0.0023)

ROA

−0.1935***

(0.0287)

−0.3432***

(0.0321)

−0.2232***

(0.0407)

−0.3678***

(0.0270)

−0.1090***

(0.0106)

−0.1125***

(0.0135)

CAPINT

−0.0150**

(0.0078)

−0.0084***

(0.0316)

−0.0550***

(0.0099)

−0.0679***

(0.0145)

−0.0033***

(0.0010)

−0.0030***

(0.0005)

INVINT

0.0130

(0.0102)

0.0133***

(0.0279)

−0.0099

(0.0150)

−0.0199**

(0.0264)

0.0008

(0.0017)

0.0026

(0.0003)

STR

0.5212***

(0.0811)

0.5243***

(0.0454)

0.2057**

(0.1120)

0.2204***

(0.0252)

−0.0498***

(0.0120)

−0.0473***

(0.0008)

GROWTH

−0.0045***

(0.0018)

−0.0038***

(0.0259)

−0.0068***

(0.0024)

−0.0075**

(0.0152)

0.0001

(0.0002)

0.0002

(0.0001)

  1. Between parentheses appear standard errors (in linear models) and the observed significance test (\(\hat{\delta }_{k}\)) statistics (in the case of ANNs). Dummies for country, sector, and year included. ***, **, and * denote significance (at 1%, 5%, and 10%, respectively) of the observed significance test statistics (t-statistics in the linear models, \(\hat{\delta }_{k}\)-statistics in the case of ANNs). All variables are defined in the Appendix.