We develop and estimate a model of dynamic interactions in which commitment is limited and contracts are incomplete to explain the patterns of income and consumption growth in village economies of less developed countries. Households can insure each other through both formal contracts and informal agreements, that is, self-enforcing agreements specifying voluntary transfers. This theoretical setting nests the case of complete markets and the case where only informal agreements are available. We derive a system of non-linear equations for income and consumption growth. A key prediction of our model is that both variables are affected by lagged consumption as a consequence of the interplay of formal and informal contracting possibilities. In a semi-parametric setting, we prove identification, derive testable restrictions and estimate the model with the use of data from Pakistan villages. Empirical results are consistent with the economic arguments. Incentive constraints due to self-enforcement bind with positive probability and formal contracts are used to reduce this probability.