I develop a model with incomplete markets, summarize the empirical facts about household investment portfolio with the National Survey of Family Income and Expenditure, a cross-sectional Japanese household survey, and estimate the structural parameters when the limited stock market participation exists. Because we cannot observe the dynamics of the individual portfolio only with the cross-sectional data, we cannot estimate the structural parameters of the dynamic model. I propose the Bayesian likelihood-free inference method to minimize both the density difference and the distance between policy functions, between the observed and the simulated values. We can find that the estimated relative risk aversion is around four. The estimation outcome implies that the model can mimic the observed household finance behavior well and the equity premium puzzle comes of a biased estimate caused by the representative agent assumption.