When insurance markets are incomplete, non-farm enterprises (NFEs), as well as temporary migration, may offer consumption-smoothing opportunities to farmers in village economies. After experiencing uninsured negative shocks to agricultural productivity, farmers may respond by creating NFEs and allocating more work time to them. These "necessity entrepreneurs'' accumulate specialized skills that increase their productivity in the non-farm sector (e.g., through learning by doing). We outline a dynamic model of household-farm labor supply decisions where each household chooses (1) how much labor time to allocate to farming, (2) whether to operate and how much labor time to allocate to an NFE, and (3) whether to dispatch temporary migrants. Using the latest ICRISAT panel data from rural India, we confirm the main predictions of our model and structurally estimate it. In counterfactual exercises, we show how the departure from market completeness shape the labor allocation and skill distribution in village economies. The use of NFEs as a consumption-smoothing device might shed light on why households in developing countries engage in both farming and low-productivity non-farm activities.