Table 1.

Simulation Results for Weibull Outcome with Multinomial Endogenous Variables Average Absolute % Bias

Average Effects	Based on 1000 replicates of size n=5000
	True Model (%bias)	Naïve Model (%bias)	2SPS Model (%bias)	2SRI Model (%bias)
E[yxe1 =1] − E[yxe0=1]	16%	205%	28%	16%
E[yxe2 =1] − E[yxe0 =1]	2%	99%	38%	2%
E[yxe1 =1] − E[yxe1 =1]	5%	34%	42%	5%
	Based on 1000 replicates of size n=20,000
E[yxe1 =1] − E[yxe0 =1]	2%	205%	2%	2%
E[yxe2 =1] − E[yxe0 =1]	2%	97%	27%	2%
E[yxe2 =1] − E[yxe1 =1]	0%	34%	51%	0%

The value in a particular cell of the table is the average percentage absolute bias, over the 1000 simulated samples, for a particular (estimator-q, average effect-t, sample size-j) combination, and is measured as

$$\left(\sum _{\text{m}=1}^{1000}\frac{1}{1000}\frac{\text{abs}(\text{AE}{(\text{t})}_{\text{qrm}}-\text{AE}(\text{t}))}{\text{abs}(\text{AE}(\text{t}))}\right)\times 100\%$$

where AE(t) denotes the true value of the t^th effect, AE(t)_qrm is its estimated value obtained by applying the q^th method to m^th sample of the r^th sample size, with

$$\begin{array}{l}\text{q}=\text{true MLE},\text{ na}\ddot{\text{i}}\text{ve},\text{ 2SPS},\text{ 2SRP}\\ \text{t}={\text{E}[\text{y}}_{{\text{x}}_{\text{e1}}=1}]-{\text{E}[\text{y}}_{{\text{x}}_{\text{e0}}=1}],{\text{E}[\text{y}}_{{\text{x}}_{\text{e2}}=1}]-{\text{E}[\text{y}}_{{\text{x}}_{\text{e0}}=1}],{\text{E}[\text{y}}_{{\text{x}}_{\text{e2}}=1}]-{\text{E}[\text{y}}_{{\text{x}}_{\text{e1}}=1}]\\ \text{r}=5000,20000.\end{array}$$