TABLE 2.

Empirical verification of Lemma 1 with 1000 simulations (${\beta }_1=-0.5$)

		Average	Average	Average	Average	Average	Average
${\gamma }_1$	Zero rate	${\widehat{\delta }}_1$	${\bar{\pi }}_T$	${\bar{\pi }}_C$	${\widehat{\beta }}_{1,\text{CV}}$	${\widehat{\beta }}_{1,\text{MLE}}$	${\widehat{\beta }}_{1,\text{ZIBC}}$
$-0.5$	0.2	$-0.045$	0.119	0.155	$-0.460$	$-0.505$	$-0.502$
	0.4	$-0.162$	0.300	0.400	$-0.346$	$-0.508$	$-0.499$
	0.6	$-0.277$	0.505	0.617	$-0.230$	$-0.507$	$-0.488$
	0.8	$-0.359$	0.736	0.810	$-0.154$	$-0.514$	$-0.488$
0	0.2	$-0.001$	0.144	0.135	$-0.504$	$-0.505$	$-0.494$
	0.4	0.000	0.358	0.350	$-0.506$	$-0.507$	$-0.493$
	0.6	$0.003$	0.568	0.562	$-0.512$	$-0.509$	$-0.496$
	0.8	0.003	0.778	0.775	$-0.523$	$-0.520$	$-0.511$
0.5	0.2	0.039	0.166	0.115	$-0.545$	$-0.505$	$-0.484$
	0.4	0.153	0.414	0.302	$-0.660$	$-0.507$	$-0.483$
	0.6	0.282	0.631	0.506	$-0.795$	$-0.513$	$-0.501$
	0.8	0.391	0.821	0.738	$-0.910$	$-0.519$	$-0.522$