This dissertation analyzes firm growth and household insurance in an economy with financial frictions. The first chapter examines the role that venture capital (VC) plays in helping promising startups achieve high growth. Three facts are documented from administrative US Census data and proprietary VC datasets. First, VC-backed firms have a particularly high chance of achieving high growth compared to non-VC-backed firms. Although only around 0.2% of all firms in the United States raise VC financing, VC-backed firms account for around 10-15% of aggregate growth in employment and payroll. Second, VC-backed startups make large upfront investments relative to startups using other forms of financing, measured in the amount of money raised and R&D expenditures. Finally, venture capitalists acquire around 3.3% extra equity stakes relative to Angel investors, conditional on the characteristics of financing deals. Based on the evidence, a firm dynamics model is developed with endogenous firm productivity and choice of financing from VC, Angel (non-VC-equity) investors, and banks. Venture capitalists provide equity-based funding and managerial advice, but they are in limited supply in the economy. The model shows the benefit of VC and Angel financing over bank financing for high-potential firms because of their large investment in innovation, which creates a debt repayment issue with bank financing when innovation is unsuccessful. VC-backed firms achieve substantial growth as a result of endogenous sorting, equity-based funding, and managerial advice. The calibrated model implies that venture capitalists' advice accounts for around one-fourth of the growth of VC-backed firms. Finally, policy experiments predict that subsidies to innovation expenditures or equity investments enhance aggregate output and consumption in the steady state in contrast to bank loan subsidies. The second chapter, joint with Dirk Krueger and Harald Uhlig, examines how households insure themselves against idiosyncratic income risk and aggregate risk. We analyze a neoclassical growth model in which risk sharing is endogenously constrained by one-sided limited commitment. Households trade a full set of contingent claims that pay off depending on both idiosyncratic and aggregate risk, but limited commitment prevents households from short-selling these assets. Under suitable restrictions of the parameters, the model results in partial consumption insurance in equilibrium. With log-utility and idiosyncratic income shocks taking two values, one of which is zero (e.g., employment and unemployment), we show that the equilibrium can be characterized in closed form despite the fact that it features a non-degenerate consumption and wealth distribution. We use the tractability of the model to analytically study inequality over the business cycle and asset pricing. In particular, we provide conditions under which the equity premium in the limited-commitment model coincides with that in the standard representative agent model. Furthermore, an extended version of the model with stochastic capital depreciation generates a sizable equity premium, significantly larger than that of the representative agent version of the model and closer to the data.