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Table 2 First stage GMM results baseline specification
S. Frey, J. Grammig
Ticker α γ λ μ J(9) p-value
LIN 0.0228 (118.1) −0.0185 (55.5) 0.5728 (134.6) 0.0003 (3.1) 0.5 1.000
DPW 0.0025 (149.8) −0.0063 (47.0) 1.8362 (150.0) −0.0001 (3.3) 21.0 0.013
HEN3 0.0415 (95.8) −0.0178 (40.1) 0.3937 (114.0) −0.0003 (1.9) 23.2 0.006
MEO 0.0132 (135.1) −0.0163 (66.1) 0.9066 (166.7) 0.0000 (0.4) 25.3 0.003
LHA 0.0019 (159.7) −0.0072 (63.6) 2.3210 (150.8) 0.0001 (4.4) 31.2 0.000
MAN 0.0104 (121.9) −0.0151 (61.8) 0.9445 (134.5) 0.0004 (5.2) 35.2 0.000
DB1 0.0162 (114.5) −0.0158 (46.7) 0.7739 (114.1) 0.0001 (1.1) 45.0 0.000
FME 0.0456 (85.0) −0.0210 (34.8) 0.3839 (96.4) 0.0000 (0.0) 53.2 0.000
TUI 0.0054 (130.3) −0.0095 (50.6) 1.3215 (127.0) −0.0002 (2.7) 57.4 0.000
ALT 0.0224 (121.9) −0.0144 (50.5) 0.5785 (142.4) −0.0002 (2.1) 79.8 0.000
CBK 0.0016 (164.0) −0.0048 (50.4) 2.4055 (152.0) −0.0001 (2.0) 81.1 0.000
CONT 0.0131 (116.6) −0.0168 (60.4) 0.8166 (139.6) 0.0002 (2.2) 85.8 0.000
ADS 0.0549 (113.2) −0.0183 (38.1) 0.3528 (141.0) −0.0002 (1.5) 118.2 0.000
BMW 0.0053 (173.8) −0.0087 (69.6) 1.2029 (203.0) −0.0001 (2.9) 173.7 0.000
TKA 0.0024 (148.6) −0.0075 (61.0) 1.9075 (158.9) 0.0000 (1.3) 206.6 0.000
SCH 0.0106 (135.3) −0.0101 (49.6) 0.8250 (168.8) 0.0000 (0.4) 232.6 0.000
RWE 0.0053 (212.2) −0.0095 (86.2) 1.2460 (210.3) 0.0001 (3.3) 239.4 0.000
DTE 0.0002 (303.0) −0.0010 (32.1) 5.0499 (232.7) 0.0000 (0.0) 292.8 0.000
IFX 0.0004 (196.7) −0.0023 (45.6) 4.5335 (170.6) 0.0000 (0.4) 360.9 0.000
HVM 0.0015 (109.0) −0.0043 (40.1) 2.8391 (130.9) 0.0000 (1.0) 363.8 0.000
VOW 0.0065 (21.2) −0.0099 (17.7) 1.0472 (195.8) 0.0001 (0.2) 429.9 0.000
BAY 0.0024 (216.9) −0.0046 (59.2) 1.6352 (225.8) 0.0000 (1.2) 458.2 0.000
BAS 0.0056 (219.9) −0.0077 (77.4) 1.1206 (244.1) 0.0000 (1.1) 683.1 0.000
EOA 0.0060 (219.2) −0.0070 (65.0) 1.0663 (252.7) 0.0000 (1.0) 1,011.3 0.000
DCX 0.0031 (258.2) −0.0049 (65.4) 1.5638 (254.9) 0.0002 (7.2) 1,376.9 0.000
SAP 0.0370 (212.6) −0.0147 (49.5) 0.5030 (237.4) 0.0006 (5.9) 1,609.9 0.000
MUV2 0.0196 (212.1) −0.0106 (60.4) 0.6476 (246.9) 0.0001 (1.0) 2,101.9 0.000
DBK 0.0065 (248.7) −0.0061 (57.7) 1.1517 (256.1) 0.0000 (0.9) 2,584.6 0.000
ALV 0.0187 (232.7) −0.0080 (35.9) 0.6453 (294.4) −0.0002 (4.5) 2,701.8 0.000
SIE 0.0052 (273.3) −0.0039 (36.4) 1.1442 (297.3) 0.0001 (2.9) 3,827.8 0.000
2×4 quotes from the bid and ask side of the visible book are used to construct update and break
even conditions derived from the zero marginal expected profit condition as in Såndas (2001).
The numbers in parentheses are t-values. The fifth and sixth column report the GMM J statistic
and the associated p-value. The stocks are sorted by ascending order of the J-statistic
break even conditions, eight update conditions, and the moment condition (6).
Order sizes X t are expressed in 1,000 shares.
Table 2 contains the first stage GMM results. 13
We report parameter estimates, t-statistics and the value of the GMM J-statistic
with associated p-values. Under the null hypothesis that the moment conditions are
correctly specified, the J-statistic is asymptotically χ 2 with degrees of freedom
equal to the number of moment conditions minus the number of estimated
13 Two stage and iterated GMM estimates are similar and therefore not reported to conserve space.
To compute the parameter standard errors and the J-statistic we employ the Bartlett Kernel with
bandwidth equal to ten lags when computing the spectral density matrix. We have tested various
lags and the results are robust with respect to bandwidth choice.