This thesis proposes an alternative procedure to test the validity of the complete markets hypothesis, that is, the assumption that the consumption of households is fully insured against idiosyncratic income shocks. This procedure looks at the implications of incomplete markets on aggregate variables, instead of looking at micro-level data, as is common in the macroeconomic literature. The testing procedure relies on the estimation of a New Keynesian model with limited household heterogeneity as in Ravn and Sterk (2016) using Bayesian estimation techniques. As demonstrated by this thesis, introducing additional estimating equations consistent with the model can improve the identification of the parameters in the model. Without assuming that the estimated models are complete in an econometric sense, this thesis shows that the model with market incompleteness does not provide a significant improvement in explaining population characteristics of aggregate variables when compared to the traditional representative agent variant, and as such, cannot reject that markets are complete based on aggregate variables only. This is despite the fact that estimating the representative agent model introduces considerable biases and misspecification error and is likely caused by the notion of household heterogeneity in the model being too limited.