This article examines the relationship between Population Growth (PG) and Economic Growth (EG) in the framework of simultaneous structural equation models. Based on Lewbel (2012), the structural parameters can be estimated using the Generalized Method of Moments (GMM). Identification requires a heteroscedastic covariance restriction that appears in some models of endogeneity, measurement errors and panel data. This study obtains several findings. First, the current and lagged variables of PG negatively and positively affect EG in the short run. Second, PG does not significantly influence EG in the long run. Third, the reverse relations running from EG to PG are weak in both the short and long run, regardless of economic development conditions.