This dissertation consists of two chapters that explore how micro-level heterogeneity helps us understand the dynamics of macroeconomic variables. Chapter 2 shows that the evolving likelihood of marriage and divorce is an essential factor in accounting for the changes in housing decisions over time in the United States. I build and estimate a life-cycle model of single and married households who face exogenous age-dependent marital transition shocks and then conduct a decomposition analysis between 1970 and 1995. The results show that household formation shocks could account for about 30% of the increase in the single's homeownership rate and play a crucial role in generating the observed sign of change in portfolio share of married households. The extended analysis on recent years after 1995 shows that the continuing decrease in marriage prospects contributed to push up the single's homeownership rate during the housing boom in the mid 2000s. Chapter 3 develops a state-space model with a state-transition equation that takes the form of a functional vector autoregression and stacks macroeconomic aggregates and a cross-sectional density. The measurement equation captures the error in estimating log densities from repeated cross-sectional samples. The log densities and the transition kernels in the law of motion of the states are approximated by sieves, which leads to a finite-dimensional representation in terms of macroeconomic aggregates and sieve coefficents. We illustrate how the model works based on the simulation of the Krusell-Smith economy and conduct an empirical analysis on the joint dynamics of technology shocks, per capita GDP, employment rates, and the earnings distribution.