This paper shows that trade integration and financial constraints can make specialization history-dependent even when sectors have the same long-run productivity potential. I develop a dynamic multisector general equilibrium model with heterogeneous entrepreneurs facing persistent productivity shocks. Financial frictions make firms' ability to expand depend on their wealth, which connects sectoral production and growth to wealth distribution. In a closed economy, relative prices respond to scarcity: initially disadvantaged sectors become more profitable and catch up with initially favored sectors. In an open economy, international markets limit this price response; initially favored sectors accumulate more wealth and account for larger long-run shares of production. I conduct a quantitative analysis using data on Peruvian firms, households, national accounts, tariffs, and international trade, and show that tighter financial constraints and greater trade exposure amplify the persistent effects of initial differences in capital allocation on sectoral specialization.