Table 2 Bias Test Results, 1979–2019
 MZ TestHP Test
 Equation [1]RestrictionsEquation [1]
 Embedded ImageEmbedded ImageEmbedded Image = 0Embedded Image = 1Embedded Image = (0,1)Embedded Image
Indiana
Top2.123
(1.499)		0.633
(0.647)		2.0060.3221.1491.950
(1.633)
Average2.572
(1.070)		1.260
(0.391)		5.777*0.4423.577*2.638
(1.371)
Poor3.668
(1.064)		0.981
(0.346)		11.897**0.0035.952**3.667**
(1.211)
Transitional0.867
(2.328)		0.361
(0.604)		0.1391.1210.792–0.683
(1.530)
North
Top2.200
(1.118)		1.436
(0.320)		3.8701.8512.7462.292
(1.432)
Average2.959
(1.135)		1.070
(0.372)		6.791*0.0363.525*2.954*
(1.377)
Poor3.909
(1.200)		0.851
(0.338)		10.608**0.1935.485**3.913**
(1.179)
Northeast
Top2.487
(1.204)		1.302
(0.486)		4.265*0.3872.6642.514*
(1.236)
Average3.616
(1.145)		0.893
(0.485)		9.966**0.0495.132*3.610**
(1.105)
Poor5.014
(1.131)		0.855
(0.361)		19.659**0.16010.284**5.078**
(1.084)
West Central
Top1.835
(1.223)		1.193
(0.467)		2.2530.1711.4061.924
(1.919)
Average2.369
(1.011)		1.215
(0.496)		5.486*0.1892.9712.459
(1.791)
Poor3.674
(1.283)		0.875
(0.533)		8.202**0.0554.136*3.645*
(1.652)
Central
Top1.950
(1.240)		0.789
(0.365)		2.4740.3351.244*1.914
(1.567)
Average2.060
(1.047)		1.010
(0.412)		3.8740.0011.9612.063
(1.394)
Poor3.114
(1.029)		0.746
(0.401)		9.161**0.3994.727*3.066*
(1.112)
Southwest
Top2.153
(1.422)		1.542
(0.713)		2.2940.5773.561*2.386
(1.251)
Average2.894
(1.535)		0.780
(0.566)		3.5560.1512.2132.793
(1.435)
Poor4.126
(1.481)		0.777
(0.514)		7.763**0.1893.882*4.116**
(1.488)
Southeast
Top2.213
(1.290)		1.447
(0.658)		2.9420.4623.369*2.466*
(1.125)
Average2.485
(1.236)		1.251
(0.633)		4.0450.1572.9502.655*
(1.095)
Poor3.238
(1.237)		0.825
(0.577)		6.858*0.0923.487*3.121*
(1.207)

  • Note: Standard errors in parentheses are heteroskedasticity and autocorrelation consistent.

  • ↵**,* Significance at the 1% and 5% levels, respectively.