This paper presents simulation evidence on the performance of the Poisson pseudo-maximum likelihood (PPML) estimator in the context of gravity equations and constant elasticity models. Santos-Silva and Tenreyro (2006) showed that the PPML estimator is well behaved in various situations, including the presence of measurement error. However, their simulations did not include data with a large proportion of zeros, which is common in trade data. This paper addresses this gap by generating data as a finite mixture of gamma variates, which naturally includes many zeros and is compatible with constant elasticity models. The simulations show that the PPML estimator performs well even when the dependent variable has a large proportion of zeros. The PPML estimator is generally well behaved, with maximum bias less than 3.5% in some cases. The gamma pseudo-maximum likelihood (GPML) estimator also performs well, but it has larger biases in some cases. The PPML estimator is more robust to departures from the implicit heteroskedasticity assumptions. The paper also compares the PPML estimator with other estimators, including the truncated-at-zero OLS estimator, the OLS estimator using ln(y_i + 1), and the threshold Tobit estimator. These estimators have large biases that do not vanish with increasing sample size, confirming their inconsistency. The results confirm that the PPML estimator is generally well behaved, even when the conditional variance is far from being proportional to the conditional mean. The presence of zeros does not affect the performance of the estimator, and in fact, the zeros are an additional reason to use the PPML estimator because other estimators based on the log-linearization of the gravity equation have to use unreasonable solutions to deal with these observations. The paper concludes that the PPML estimator is a promising workhorse for the estimation of constant elasticity models such as the gravity equation.This paper presents simulation evidence on the performance of the Poisson pseudo-maximum likelihood (PPML) estimator in the context of gravity equations and constant elasticity models. Santos-Silva and Tenreyro (2006) showed that the PPML estimator is well behaved in various situations, including the presence of measurement error. However, their simulations did not include data with a large proportion of zeros, which is common in trade data. This paper addresses this gap by generating data as a finite mixture of gamma variates, which naturally includes many zeros and is compatible with constant elasticity models. The simulations show that the PPML estimator performs well even when the dependent variable has a large proportion of zeros. The PPML estimator is generally well behaved, with maximum bias less than 3.5% in some cases. The gamma pseudo-maximum likelihood (GPML) estimator also performs well, but it has larger biases in some cases. The PPML estimator is more robust to departures from the implicit heteroskedasticity assumptions. The paper also compares the PPML estimator with other estimators, including the truncated-at-zero OLS estimator, the OLS estimator using ln(y_i + 1), and the threshold Tobit estimator. These estimators have large biases that do not vanish with increasing sample size, confirming their inconsistency. The results confirm that the PPML estimator is generally well behaved, even when the conditional variance is far from being proportional to the conditional mean. The presence of zeros does not affect the performance of the estimator, and in fact, the zeros are an additional reason to use the PPML estimator because other estimators based on the log-linearization of the gravity equation have to use unreasonable solutions to deal with these observations. The paper concludes that the PPML estimator is a promising workhorse for the estimation of constant elasticity models such as the gravity equation.