We introduce household heterogeneity into a small open economy New Keynesian model and estimate the model on South Korean data using a Bayesian likelihood approach. The model features uninsurable idiosyncratic income risk, sticky nominal wages and prices, liquid and (partially) illiquid foreign and domestic assets, government stabilization through monetary and fiscal policies, and international trade in goods and assets. The economy is perturbed by a mix of aggregate domestic shocks deriving from both technological parameters and from economic policy, and international shocks to the demand of goods and to the return of liquid and illiquid foreign assets. We show that international shocks are important determinants of fluctuations in Korea including key aspects of inequality.